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A TEXT- BOOK OF 
LOGIC 



BY 

ARTHUR ERNEST DAVIES 

PROFsasoR or Philosophy in The Ohio State University 



(tialnmbm. <&t?ta 

R. G. ADAMS AND COMPANY 
1915 



COPYRIGHT, 1915 

BY 

ARTHUR ERNEST DAVIES 



DEC -6 1915 

©CI.A4I6749 



-^ 



% 



y 



TO 
MY FATHER 






1 






PREFACE 

The time has not arrived when it is possible or 
desirable to write a text-book of logic for elementary- 
students which departs very considerably from the 
course that has been defined by university require- 
ments in various parts of the world. Both in Eu- 
rope and in America instruction in this subject has 
to a large extent been controlled by what may be 
called the classical tradition of which Aristotle and 
Mill are the two fountain heads. In some quarters 
this fact has operated as a hardship, and has led 
to open, if rather one-sided, criticism of the subject's 
educational usefulness, on the one hand, and has 
directed attention to and aroused interest in the 
real and supposed defects of the traditional logical 
doctrine, on the other. The position both of those 
who maintain the conservative attitude, and of those 
who would substitute for the old some new kind of 
logic, is capable of defence up to a certain point, 
and there is no doubt that the stirring of the aca- 
demic waters on this subject will result at some 
time in a larger freedom in the choice of the mate- 
rial and methods of logical instruction, and to that 
extent will reduce the possibility of attributing to 
the subject the imperfections of temper and under- 
standing of those who teach it. 

I hold no brief for traditionalism in logic, and 
while I sympathise with and, according to my 

vii 



Vlll PREFACE 

ability, appreciate the value of much that the advo- 
cates of the newer logics have contributed to our 
knowledge of the methods by which the human 
mind reaches truth, I have never been able to dis- 
possess myself of the belief that the older logic 
in some measure had enabled me to understand what 
the newer logic had to say. Were I an artist, it 
would be my desire to paint the ocean, just because, 
I imagine, it is so constantly changing and withal 
so eternally the same> A similar interest may 
stimulate one to observe, in all the ways that modern 
logic is making familiar to us, the wonderful change- 
fulness and practical resourcefulness of the mind's 
approach to truth; but if one were to identify logic 
with the observation and description of these shift- 
ing phenomena, he would be in the position of the 
man for whom the ocean was no more than the 
waves that rose and fell and broke upon its bosom. 
The human mind has a determinate structure, and 
it is with that structure, so far as it is displayed in 
the field of knowledge, that logic aims to make us 
acquainted. And I do not believe that it has been 
reserved for our own times to utter the only true 
words on this subject, nor that we can afford to neg- 
lect the teaching of the ancients. Aristotle defined 
logic and formulated many of its methods in a way 
that has given life to the subject for over two thou- 
sand years, and much that is modern takes its point 
of departure, either by way of criticism or refining, 
from what he wrote in the beginning of the science's 
existence. It is not to be understood, of course, 



PREFACE IX 

that the traditional doctrine stands in no need of 
critical examination. The reverse is the fact. The 
enormous increase of knowledge in the modern era 
makes it necessary. But how are criticism and 
revision possible if the subject is, as some seem to 
think, wholly illusory, or if we remain in absolute 
ignorance of the doctrine upon which criticism and 
revision are to be directed? 

It seems, therefore, that for some time to come 
logic will continue, in the main, to be traditional, 
and that books of logic will have to conform to the 
requirements that are determined by that fact. 
But there are all sorts and degrees of conformity, 
and I confess to a liking for that kind and degree 
which is not inconsistent with the exercise of the 
largest liberty of one's academic conscience. It 
would not be surprising, consequently, if it were 
discovered that I had allowed the present situation 
in logic to sit lightly upon me, and that, where it 
seemed desirable, I had departed in method and doc- 
trine from traditional views. It is I believe in some 
such way as this, rather than in assuming a critical, 
not to say captious, attitude toward the whole of 
traditional logic that the best interests both of the 
subject and of those who study it can be advanced. 

It is hardly necessary to say that the present 
book as a whole is the product of experience in 
teaching logic to elementary and advanced students 
of the subject, No one, I am convinced, should 
attempt to write a text-book in any subject, and 
certainly not in logic, who has not learned in the 



X PREFACE 

practical way of teaching it where its main difficul- 
ties are found, and who has not had an oppor- 
tunity afforded him of devising methods of overcom- 
ing them. For, in the first place, a text-book must be 
written for the student, that is, for one who is 
presumed not to know anything about the subject 
of which it treats and, for him, the greatest service 
that it can render is to stimulate an interest in the 
problems with which it deals. But also it should 
be an instrument in the hands of the teacher which 
facilitates the task of teaching, and adapts itself 
to the purposes that he may hold before himself 
and the class. However far my book may be from 
completely fulfilling these objects, I hope it has 
entirely escaped the capital offence of substituting 
itself, in the regard and thought of the student, for 
the teacher, and that it can not be accused of 
helping to degrade the teaching function to the 
mere level of hearing a recitation. I trust, there- 
fore, that there are many sections that will be 
found to require the generative touch of the teacher, 
and that what in his hours of preparation may 
appear to the student as a valley of dry bones will 
be vitalized by the teacher into living forms in the 
hours spent in the lecture room. 

I have given to the judgment a prominence in 
the order of topics which I think is required for a 
true comprehension of the problem of logic, and 
have distinguished between it and the proposition 
for the purpose of indicating the class of questions 
which any attempt to express our judgments in 



PREFACE XI 

words quite naturally suggests. If I am not mis- 
taken, current controversy in philosophy would 
sometimes have been simplified, if indeed the occa- 
sion for it were not entirely removed, if it had been 
distinctly recognised that the judgment is not the 
proposition, and that the problems of each are quite 
distinct. A close relationship must, of course, be 
recognised between judgments and propositions, but 
I am not without hope that the separate treatment 
of these topics will meet with the approval of my 
colleagues, although it results in placing at the 
very beginning what must be regarded as one of the 
difficult chapters of the book. I do not believe that 
the judgment chapter is insuperably difficult; it is 
not more difficult, for example, than is the neuro- 
logical material to which the psychologist introduces 
his students at the very outset of their studies. And 
I may say that the effort has been made to present 
the subject in a manner as simple as is consistent 
with the real complexity and difficulty of the prob- 
lem. With a simplification which falsifies a topic in 
the interests of easing the task of student or teacher 
I have as little sympathy as I have with the reverse 
method of creating or magnifying difficulties for the 
good of the learner's academic soul. But we must 
cultivate in ourselves and in those we teach the 
ability to recognise a difficulty when and where it 
exists, and to face it with determination, and this 
requires from teacher or pupil neither apology nor 
praise. 



Xll PREFACE 

With respect to other features of the book, I 
may, perhaps, be expected to say something in justi- 
fication of the relatively detailed account that has 
been given of the fallacies. There is, in fact, little 
to say, and that little I trust will appear quite super- 
fluous to any one who has read the chapters in 
question. Both the mode of treatment and the 
amount of space given to the subject have been 
determined by the belief that the problem of falla- 
cies has not received as a rule the recognition that 
it deserves, and that it has not been correlated to 
the main logical doctrines in a sufficiently organic 
way. I do not wish to be understood to mean that 
the chapters given here are at all adequate in these 
respects to the importance I conceive the subject 
to have. I have, however, sought to avoid leaving the 
impression that the subject has no practical or pos- 
itive significance, and have endeavoured to keep the 
whole discussion in close relation to the body of 
logical doctrine developed in the preceding chapters. 
To leave the student with some degree of respect 
for the topic as a whole seems to me to be decidedly 
worth attempting, especially when the student is 
one who is making acquaintance with the subject 
for the first time. It will also be found, I think, 
that the two chapters in which the fallacies are dis- 
cussed lend themselves readily to the purposes of a 
review of the main logical problems, and that the 
new point of view from which these problems are 
considered, the point of view, namely, of the sources 
of error that lurk in the processes of logical thinking, 



PREFACE Xlll 

will not only relieve the review from the banalities 
that usually attach to a twice performed task, but 
may be found to make the problems themselves more 
articulate and significant. At any rate, if we begin 
our logical studies with the object of finding out 
what is meant by truth, and what are some of the 
forms in which truth exists, one would think that 
a discussion of error or at least an examination of 
some of the forms in which error exists, would 
serve to emphasise the importance and the character 
of logical problems. And, I confess, it seems ro me 
that no amount of technical skill in the manipulation 
of technical formulas can compensate for any failure 
to perceive that the problems of logic originate in 
the effort to think and to express ourselves clearly 
and correctly, and that, therefore, the science that is 
devoted to the study of the principles of clear and 
correct thinking is one in which any person that has 
any pretense to education should have an interest. 
And in this connection I may add that the questions 
on the text appended to each chapter are designed 
as much to stimulate such an interest as to test a 
student's acquaintance with the details of the dis- 
cussion; and if any apology for printing them or 
for making them so numerous is needed, I can only 
reply that my own students say that they have 
found them useful. 

I confess to a certain compunction in offering 
to the public a book on logic which fails to discuss 
in a systematic way the so-called laws of thought, 
although I have never felt the necessity of apolo- 



XIV PREFACE 

gising to myself for failing to expound to my ele- 
mentary students so recondite a subject. I really 
have never found that any attempt to interest be- 
ginners in logic in this problem was satisfactory 
either from my own or from their point of view. 
The book, therefore, does in this particular conform 
to my practice, and the justification that may be 
offered is that it is pedagogically and scientifically 
preferable for the student to discover some problems 
for himself in the course of his studies than to force 
them in a more or less artificial manner upon his 
attention. There are places in the text where the 
subject here in question is quite near the surface, 
and if it happens to break through, the wise teacher 
will surely not fail to take advantage of his oppor- 
tunity. 

With respect to the general outcome of such a 
course in logic as is outlined in this book, it is 
enough to say that I should be exceedingly disap- 
pointed if the way had not been prepared for an 
intelligent study of the larger treatises on the sub- 
ject, and if the door had not been opened, though 
only a little way, through which the student might 
pass to a study of the perennial problems of phil- 
osophy itself. About the former point, it is only 
necessary to say that the lists of advanced refer- 
ences at the end of the chapters, limited as they 
necessarily had to be, are intended to invite indi- 
vidual students and whole classes to read more 
widely and on a more elevated plane discussions of 
the problems which are considered in the text, and 



PREFACE XV 

to which reference is also made in the first lists of 
books. An experiment on the possibility of profit- 
ably using books of an advanced character might 
be made by the student himself in connection with 
those parts of the text which fail to interest or 
profit him. I shall not be surprised if very often 
the presumably more difficult reference turns out 
in the end to be the simpler statement. If any 
one should doubt the value of logic as an introduc- 
tory approach to the problems of philosophy, which 
is the second point mentioned above, I can only say 
that so long as those problems continue to depend, 
to the extent that they actually do, upon logical 
construction, there is absolutely no possibility 01 
understanding what the problems are, much less of 
contributing to their solution, if one has not ac- 
quired a mastery of the instruments of logical think- 
ing. But not only is this true in respect of philos- 
ophy narrowly interpreted; an acquaintance with 
logical methods is also important if we who are not 
philosophers in the techincal sense of the word are 
to take an intelligent attitude toward our own lives. 
Toward such an end, I hope some contribution has 
been made by the mode in which the logical problem 
has been conceived, and by the manner in which it 
has been worked out. 

For those who are acquainted with the liter- 
ature of the subject, it is not necessary for me to 
name the sources of my chief indebtedness, and for 
those who are not, such a proceeding would savour 
of a vain parade. I shall, therefore, content myself 



XVI PREFACE 

with the statement that I have learned from the 
masters of many schools, and have retained a grate- 
ful affection for them all. As I am not conscious of 
being a partisan, I presume that even those who 
have taught me most would hardly recognise me as 
one of their disciples. The public, consequently, will 
be in no doubt when it comes to /apportioning praise 
or blame for what is here set down, although it is 
evident, so that he who runs may read, that it is 
not all made up out of my own head. I have quoted 
when necessary, I have also paraphrased, I have 
refused neither suggestion nor illustration when any 
of these methods furthered the object I have can- 
stantly held before me in writing these pages. I 
want, therefore, to thank all who by their published 
writings have rendered themselves liable to this 
sort of literary piratage. I am also indebted to col- 
leagues for particular services which it is a pleasure 
to acknowledge. Professor Rudolph Pintner has 
read many of the chapters in the first half of the 
book, and made suggestions which have improved 
the form over that in which they were originally 
cast. Mr. A. P. Weiss made the drawings for all 
the figures, and also read some of the sections on 
induction. Professor David R. Major has read all 
the chapters in manuscript and in proof. I feel that 
his criticisms and suggestions have been invaluable. 
It is certainly not for the want of friendly and 
intelligent advice that I may sometimes have erred 
in aim and execution. The final stages of the proofs 



PREFACE XVll 

have been entirely in Dr. Major's hands. I take 
this opportunity to acknowledge assistance that has 
been generously rendered. 

Eltham, Kent. A. E. D. 

Feb. 25, 1915. 



CONTENTS 
CHAPTER I. 

THE PROBLEM OF LOGIC. pAQE 

The Starting Point 1 

Each Science has a Different Subject-Matter . . . .T7 1 

The Thought Element in Knowldge 2 

What we Mean by Knowledge 5 

Knowledge is Systematic 6 

Logic and the Knowledges 9 

The Subject-Matter of Logic 10 

Logic as Scientia Scientiarum 11 

The Humanistic Influence in Logic 12 

Relation of Logic to Psychology 14 

Logic as an Art 16 

What Logic is 18 

References 22 

Questions 22 

Exercises 23 

CHAPTER II. 

THE JUDGMENT. 

The Meaning of Thought 24 

Judgment and Thought 28 

Other Mental Attitudes Akin to Judgment 31 

Judgment and Groundless Statements 33 

Practical and Theoretical Aspects of Thought 35 

Relevant Assertion 36 

The Interest Factor in Knowledge 44 

The Object of Judgment 47 

The Universe of Discourse 50 

xix 



XX CONTENTS 

PAGE 

Truth, Probability and Error , . 58 

References 70 

Questions 70 

Exercises 74 

CHAPTER III. 

THE PROPOSITION. 

Judgment and the Proposition 76 

The Import of Propositions 79 

Formal Analysis of Propositions 84 

Terms 85 

Names and Words 88 

The Copula 91 

The Relational View 92 

The Existential View 95 

Kinds of Propositions 98 

Relations of the Main Types of Propositions 99 

References 104 

Questions 104 

Exercises 105 

CHAPTER IV. 
TERMS. 

Proposition and Terms 107 

Connotative and Denotative Use of Terms 107 

Relation of the Connotative and Denotative Use of 

Terms 110 

Distribution of Terms 114 

Some Other Characteristics of Terms 117 

Concrete Meaning 118 

Individual Meaning: Proper Names and Designa- 
tions 120 

General Meaning 124 

Collective Meaning: Individual and General 126 



CONTENTS XXI 

PAGE 

Abstract Meaning 130 

References 136 

Questions 136 

Exercises 138 

CHAPTER V. 

terms (Continued). 

The Purpose of the Chapter 139 

The Basis of the Distinctions to be Studied 139 

Absolute and Relative Meaning 140 

Positive and Negative Meaning 143 

The Conditions of Negative Meaning 145 

The Logic of Negation 149 

Privative Meaning 153 

Disparate and Contrary Meaning 155 

References 155 

Questions 156 

Exercises 157 

CHAPTER VI. 

DEFINITION AND THE PREDICABLES. 

The Questions of this Chapter 158 

Non- Ambiguity 160 

Ambiguity 162 

Translation 165 

When Translation may be Employed 166 

When Definition is Required 167 

The Method of Definition 168 

Definition per genus et differentiam 170 

Verbal and Real Definition 173 

The Relation of Purpose to Definition 175 

Tests of a Definition 176 

The Problem and Classification of the Predicables 181 

The Commensurable Predicables 183 



XX11 CONTENTS 

PAGE 

The Non- Commensurable Predicables 185 

References 186 

Questions 187 

Exercises 189 

CHAPTER VII. 

DIVISION AND CLASSIFICATION. 

Relation of Definition and Division 190 

What is Meant by Logical Division 191 

Other Kinds of Division 193 

Fundamentum Divisionis 195 

Questions of Terminology 199 

Rules of Logical Division 200 

Dichotomy 205 

The Tree of Porphyry 210 

Clasification Defined 211 

Classification and Definition 212 

Classification and Division 213 

Kinds of Classification 215 

References 218 

Questions 219 

Exercises 220 

CHAPTER VIII. 

CATEGORICAL PROPOSITIONS. 

Types of Propositions 222 

Classification of Categorical Propositions 223 

Quantity of Propositions 225 

The Singular Proposition 228 

The Universal Proposition 229 

Kinds of Universal Proposition , 230 

The Particular Proposition 230 

The Indesignate Proposition 232 



CONTENTS XX111 

PAGE 

Quality of Propositions 234 

The Affirmative Proposition 235 

The Negative Proposition 236 

The Relation of Affirmative and Negative Propo- 
sitions 238 

Exceptive and Exclusive Propositions 240 

Compound Propositions 244 

Modality of Propositions 246 

The Assertoric Proposition 247 

The Problematic Proposition 248 

The Apodeictic Proposition 250 

References 251 

Questions 252 

Exercises 253 

CHAPTER IX. 

IMPLICATIONS OF CATEGORICAL PROPOSITIONS. 

Relation of Quantity and Quality in Categorical Propo- * 
sitions 255 

Structural Formulae Indicating the Quantity and Qual- 
ity of Propositions 256 

Distribution of the Terms of the Four Categorical Propo- 
sitions 259 

Meaning and Classes of Implication 263 

The Opposition of Propositions 265 

Contrariety 266 

Subalternation 269 

Contradiction 272 

Subcontrariety 273 

The Square of Opposition 275 

Nature and Methods of Eduction 278 

Obversion 279 

Conversion 283 

Contraposition 288 

Inversion 290 



Xxiv CONTENTS 

PAGE 

Summary of Eductions 291 

References . 293 

Questions 293 

Exercises 296 

CHAPTER X. 

CATEGORICAL ARGUMENTS. 

The Problem of the Chapter 297 

Two Preliminary Questions 298 

Nature of the Syllogism 301 

Structural View of the Syllogism 303 

Rules of the Syllogism 305 

Figures of the Syllogism 310 

Special Rules of the Four Figures 312 

The Moods of the Syllogism 315 

The Valid Moods of the Syllogism 316 

Relation of Moods to Figure 318 

References 322 

Questions 323 

Exercises 324 

CHAPTER XI. 

OTHER FORMS OF CATEGORICAL ARGUMENT. 

Their Relation to the Syllogism 326 

Enthymeme 328 

Polysyllogism 329 

Types of Polysyllogism 331 

Sorites 332 

Epicheirema 335 

References 336 

Questions 337 

Exercises 338 



CONTENTS XXV 

CHAPTER XII. 

DISJUNCTIVE AND HYPOTHETICAL PROPOSITIONS AND 

ARGUMENTS. „ Ariw 

The Disjunctive Proposition 340 

The Nature and Classes of Disjunctive Syllogism 343 

The Moods of the Disjunctive Syllogism 344 

The Validity of Disjunctive Arguments 345 

The Hypothetical Proposition 347 

The Hypothetical Syllogism 348 

The Moods of the Hypothetical Syllogism 350 

Dilemmas 354 

Classes of Dilemma 357 

The Validity of the Dilemma 359 

References 361 

Questions 362 

Exercises 364 

CHAPTER XIII. 

INDUCTION AND METHODS PRELIMINARY TO INDUCTION. 

General Statement of the Problem 366 

What is Meant by Fact 367 

Nature of Reality 370 

Induction by Simple Enumeration 372 v 

The Value of Simple Enumeration 375 

Empirical Generalisation 376 

Colligation of Facts 378 

Parity of Reasoning 380 

References 381 

Questions 382 

Exercises 384 

CHAPTER XIV. 

SOME DESCRIPTIVE METHODS OF INDUCTION. 

Relation of Numbers of Instances to an Induction ...... 385 

Logical Significance of Statistical Methods 389 

Qualitative Methods of Observation 393 



XXVI CONTENTS 

PAGE 

The Nature of Scientific Observation 395 

Experimental Observation 400 

References 403 

Questions 404 

Exercises 405 

CHAPTER XV. 

SOME EXPLANATORY METHODS OF INDUCTION. 

The Nature of Scientific Explanation 406 

The Meaning of Analogy 409 

The Logical Character of Analogy 411 

The Function of Analogy in Induction 416 

The Nature of Hypothesis 419 

Objections to the Use of Hypothesis 422 

Verification of Hypotheses 427 

Hypothesis and Theory 429 

References 431 

Questions 432 

Exercises 434 

CHAPTER XVI. 

CAUSATION. 

General Statement of the Problem 435 

The Practical Aspect of the Problem 436 

The Theoretical Aspect of the Problem 438 

The Genetic Relation of the Practical and Theoretical 

Views 440 

The Origin and Nature of the Causal Problem 442 

The Course of Our Further Discussion 444 

The Time Relations of Causal Events 445 

The Complex Character of Causal Events 449 

The Necessity of Causal Events 456 

The Plurality of Causes 461 

References . . . 467 

Questions 468 

Exercises 470 



CONTENTS XXV11 

CHAPTER XVII. 

MILL'S EXPERIMENTAL METHODS. 

Their Historical Position 471 

The Nature of the Problem to Which These Methods 

Apply 473 

Elimination as a Method of Causal Inquiry 474 

The Method of Agreement 477 

The Method of Difference 482 

The Joint Method of Agreement and Difference 486 

The Method of Concomitant Variations 492 

The Method of Residues 496 

References 501 

Questions 501 

Exercises 504 

CHAPTER XVIII. 

FALLACIES. 

Fallacy Defined 508 

Classification of Fallacies 511 

Fallacies of Interpretation ; 514 

Verbal Ambiguity 515 

Equivocation 515 

Accent 517 

Composition 518 

Division 519 

Accident 520 

The Converse Fallacy of Accident 521 

Structural Ambiguity 522 

Amphibole 522 

False Parenthesis 524 

Fallacies of Implication 525 

Fallacies of Opposition 526 

Fallacies of Eduction 529 



XXV111 CONTENTS 

PAGE 

Fallacies of Inference 531 

The Deductive Fallacies 533 

Categorical Fallacies 533 

Fallacies of Four Terms 534 

Fallacies of Insufficient Premises 537 

Hypothetical Fallacies 539 

Disjunctive Fallacies 544 

References 548 

Questions 548 

Exercises 550 

CHAPTER XIX. 

fallacies (Continued). 

Inductive Fallacies 552 

Fallacies of Language 553 

Fallacies of Observation 555 

Fallacies of Explanation 563 

Fallacies of the Context 567 

Fallacies of Assumption 569 

Petitio Principii 570 

Complex Questions 572 

Ignoratio Elenchi 573 

Non Sequitur 576 

Fallacies of Interest 578 

References 584 

Questions 585 

Exercises 587 



CHAPTER I 

THE PROBLEM OF LOGIC 

The Starting Point. It is customary to begin the 
exposition of a branch of knowledge with a state- 
ment and explanation of its definition. This is a 
useful mode of procedure when it can be presumed 
that those for whom one writes have previously 
acquired an elementary knowledge of the subject to 
which the definition relates. But since no such pre- 
sumption is made in regard to those who may be 
expected to read this book, we shall postpone for 
the present the task of formulating a definition of 
logic. Meanwhile, we shall discuss a number of 
topics, all of which throw light upon some feature 
of the problem of logic, and each of which will con- 
tain suggestions as to the nature of the subject to 
the exposition of which this book is devoted. And 
we shall find it convenient to begin our discussion of 
these topics by asking what is the subject-matter 
of which logic, in all its various stages and branches, 
is the study. 

Each Science has a Different Subject-Matter. It 
will, perhaps, help to emphasize the importance of 
this inquiry if we recall, first, that a science presup- 
poses the existence of a special kind of material, 
called its subject-matter; and, second, that each 
science has a different subject-matter. For example, 
in geology we learn about the structure of the earth's 

(i) 



2 A TEXT-BOOK OF LOGIC 

surface ; in physiology, about the functions of living 
organisms. Physics is a study of bodies in motion ; 
and geometry, of figures in space. In these, and in 
similar cases, the subject-matter of the science is 
the material which the scientist observes and de- 
scribes. 

The Thought Element in Knowledge. If we con- 
sider further how the several sciences are con- 
stituted, it soon becomes evident that the mate- 
rial selected for study is only one condition of 
the existence of a science. The scientist must also 
think about his material before his knowledge con- 
cerning it can have the characteristics of scientific 
knowledge. He must, for one thing, arrange, or, as 
it is said, classify, the material that he has collected. 
It is not, however, the purpose of this section to 
describe the methods that the scientist employs in 
studying his material. At present, we wish to call 
the student's attention to the fact that the attainment 
of any kind of knowledge is impossible without an 
active exercise of the thinking processes, and to 
warn him that the passive flow of images and ideas 
through consciousness must not be mistaken for 
thinking. It is true that without images and ideas 
there can be no thought; but thinking consists in 
comparing objects with one another, in differen- 
tiating the like from the unlike, in combining them 
into more complex wholes, in relating in many and 
diverse ways these wholes to each other, etc. Think- 
ing, in other words, is a specialised sort of mental 
activity, an activity that taxes to the utmost, and 



THE PROBLEM OF LOGIC 3 

frequently brings into play, all the abilties with 
which the human mind is endowed. It is the supreme 
task to which the many have been called; but 
if we regard it lightly, or presume that it can be 
accomplished without toil, or if we erect our own 
incapacity or indolence into a reason for the useless- 
ness of the endeavor, we must abandon the hope of 
joining the company of the few who are chosen. It 
is, therefore, with good reason that logic directs 
attention to the function of thought in human knowl- 
edge, for thinking is the one way, the only royal 
road, to the goal of an educated life. To think about 
the objects of one's experience is, then, necessary 
if knowledge is to exist; but thinking, it must also 
be borne in mind, is "not a passive suffering of some- 
thing, but a doing of something with" these objects. 
Or, as Wundt has expressed it, "jedes denken ein 
Wollen." 

Not only, then, must we think if we are to attain 
scientific knowledge ; we must also think in order to 
attain knowledge that, in the strict sense, cannot be 
described as scientific. Illustrations of the truth of 
this statement may be found in history, economics, 
jurisprudence, as, indeed, it may be in all those other 
studies which, like these, are interested in the ways 
in which the various needs of men are met in a social 
organisation. It would seem, then, that wherever 
we have knowledge, whether it be in the form of the 
natural or the historical sciences, as these others 
may be called, we have a witness to the ways in 
which the demands for thought have been met. In 



4 A TEXT-BOOK OF LOGIC 

brief, unless we think about the material that obser- 
vation brings, knowledge cannot exist ; and, further, 
it is what we think that converts this material into 
definite species of knowledge. 

The following illustration may throw additional 
light upon the statements of this section, and empha- 
sise the importance of thought for all forms of 
human knowledge. We all know what a picture puz- 
zle is, — a collection of odd-shaped and variously 
coloured pieces of cardboard which, when put to- 
gether in their proper relations, form a complete 
and consistent whole. All of us, moreover, have 
experienced difficulty in putting the pieces of card- 
board together so that the hidden pattern or picture 
is made evident. If, now, we study a case like this, 
we may observe that the difficulty we had in bring- 
ing out the pattern was not due to the lack of any- 
thing in our material, — all the pieces, we shall sup- 
pose, were before us, and were capable of being 
fitted to one another in an appropriate way. But 
the task of putting them together in the proper way 
was by no means easy. Where was the source of our 
difficulty ? We cannot attribute it to our material ; 
and most of us would agree that it was due to our 
inability to see which parts should come next and 
next and next. If anyone chanced to observe us at 
our task, he probably would have heard us exclaim, 
'How stupid I am!' 'What's the matter with me!' 
'Why can't I see it!' That is to say, he would have 
heard us blaming ourselves, and finding fault with 
the things we were doing to the material with which 



THE PROBLEM OF LOGIC 5 

we were working. What bearing, one may ask, does 
this have upon the question before us? Just this, 
that if we are to solve the simplest problem, thought 
must be brought to bear upon the material which 
constitutes the subject-matter of that problem. 
When we do not succeed in doing this, and when, 
for any reason, we are baffled in our endeavour to 
make out the nature and relations of the material 
we are studying, a special emphasis is thrown upon 
the thought factor, the one which, under more favor- 
able conditions, is liable to be lost sight of entirely. 
In this we are like children who look about their 
world delightfully oblivious of the fact that the eyes 
provide them with the light of all their seeing. It is 
only when the eyes fail that one becomes conscious 
of their existence. Similarly, when knowledge fails 
an unsuspected factor of knowledge gains promi- 
nence, and to this factor, to which attention is thus 
drawn, we give the name — thought. 

What we mean by Knowledge. The student who 
has read carefully the foregoing paragraphs will 
understand what we mean when we say, — we are 
always thinking about something. The italicised 
words call attention to the two factors in knowledge. 
There is the object, — the million-starred heavens, 
or the one solitary maiden, on the one side ; and, on 
the other, our thoughts about this object. Both 
these elements — object and thought — are neces- 
sary to knowledge. Objects that no one thinks about 
are only the materials of knowledge, and thoughts 
that are not thoughts - about something in par- 



6 A TEXT-BOOK OF LOGIC 

ticular can hardly be called thoughts at all. It is 
only when our thoughts are thoughts-about-objects 
that we give them the name of knowledge. This 
statement holds so generally that by knowledge of 
any sort whatsoever — poetry or legend or history 
or science or just every-day opinion — we may be 
understood to mean our thoughts-about-objects. 
Accordingly, from the standpoint of our analysis, 
knowledge=object-f thought. In later sections, we 
shall have more to say about these two factors of 
knowledge. 

Knowledge is Systematic. If we consider our 
thoughts-about objects with some care, we shall ob- 
serve that they tend constantly to become fixed, 
orderly, and systematic. This is not an accident ; it 
is rather of the nature of a demand that we make 
upon ourselves and our fellows, so much so that we 
dismiss with a shrug of the shoulders the thoughts 
of any one who fails to meet it with a fair degree of 
success. We may say, then, that we are all alike in 
having ordered thoughts ; we differ only with respect 
to the degree of success that we attain in intro- 
ducing that particular kind of order that makes our 
thoughts most effective. For example, there is a 
great difference in the coherence of the thoughts of 
an insane or feeble-minded person and those of the 
average normal person. In the former case, we 
observe both a frequent change of the subject of his 
thought, and an obvious looseness of connection be- 
tween one thought and another, even when these 
refer to the same subject. Sometimes the only con- 



THE PROBLEM OF LOGIC 7 

nection that can be observed between one thought 
and another is the similarity in sound of the words 
in which the thoughts are expressed. On the other 
hand, we expect to find the average normal person 
able to think in such a way that the connection be- 
tween one thought and another follows the line of 
the essential connections of one part and another of 
the subject about which he thinks. When this is the 
case, we call the person's thinking 'systematic', — 
systematic, that is, in the sense that the order of his 
thoughts is warranted by the nature of the subject 
to which his thoughts refer. 

Now it may be interesting and profitable to note 
what are the conditions of systematic thinking. 
There are three that, from the logical standpoint, 
require mention. First, there is the difference, 
native and acquired, in the ability of individuals sys- 
tematically to develop by thinking any subject in 
which they may be interested. We recognise the 
fact that one person is more highly endowed in this 
respect than another in such every-day expressions 
as: 'He's just smart'; 'All there is to say is, he's 
got brains.' But we also recognise the fact that we 
are all capable of improvement, however excellent 
or mediocre our native endowment may be. The 
great national organisations for the education of the 
young are a recognition of this fact. But, of course, 
all that we can hope to do by education is to diminish 
the difference between one individual and another; 
we do not expect to overcome the advantage that 
lies on the side of the person who adds to a high 



8 A TEXT-BOOK OF LOGIC 

native endowment a careful and industrious train- 
ing. The second condition of systematic thinking 
is found in the fact that not all the subjects about 
which we think seem capable of being systematised 
with the same degree of completeness. For example, 
we do not find in the social sciences the same degree 
of coordination that we find in the natural sciences ; 
and, in a general way, we may attribute this to the 
greater complexity of the subject-matter of the for- 
mer as compared with the latter. 

It may be observed, thirdly, that not every 
occasion that calls for thought is met best with the 
strictest and most thorough exercise of our thinking 
ability. If we compare, for example, the thoughts 
of the man of business with those of the economist, 
or the thoughts of the politician with those of the 
political scientist, we shall see that they differ, not 
necessarily in proportion to the abilities of the indi- 
viduals to think, nor directly with respect to the 
difficulties of the subject-matter about which they 
think ; but the occasion that sets the thinker his par- 
ticular task sets also the limits within which the 
task is to be carried out. The same thing is true up 
and down the line of our every-day observation and 
experience. The man, for example, who carried 
over into social life the passion for precision, accu- 
racy, and completeness that properly belongs to a 
scientific publication would be voted a bore, just as 
surely as the man who worked in his laboratory with 
the leisurely and lax methods of a man of the world 
would be pronounced a failure. Circumstances alter 



THE PROBLEM OF LOGIC 9 

cases ; and logic observes that in any of the depart- 
ments of human life where thought is called for, it 
is only the degree of systematic thinking appro- 
priate to the circumstances that it is ever necessary 
to attain. 

Logic and the Knowledges. In our discussion of 
what knowledge is we have seen that knowledge may 
exist in many different forms, varieties, depart- 
ments, or branches. For example, engineering, psy- 
chology, bacteriology, literature, biology, etc., are so 
many different forms of the one thing we call knowl- 
edge. For this reason, it would be better, simpler, 
and more concrete if we were to accustom ourselves 
to speak of these subjects as 'knowledges' whenever 
we wished to refer to the plurality of the depart- 
ments of knowledge. We have a precedent for this 
usage in that we speak more often of the sciences 
than we do of science. By knowledges, therefore, 
we mean the several varieties, forms, or kinds into 
which knowledge has been observed to fall. Now 
we may observe that, historically, most of the other 
subjects of knowledge existed before logic was for- 
mulated into a science. Mathematics, astronomy, 
physics, zoology, political and social philosophy, for 
example, are must older branches of knowledge than 
logic. And if to this we add the fact that logic came 
into existence as a result of a study of the methods 
of these sciences, we shall see that it was the exist- 
ence of the knowledges that made logic possible 
rather than the existence of logic that made them 
possible. Hence, it would seem to be true that while 



Ayr* ir 



10 A TEXT-BOOK OF LOGIC 

every form of knowledge may be cultivated and may 
flourish independently of logic, logic cannot even 
begin to be unless some of the forms of knowledge 
have already established themselves. 

The Subject-Matter of Logic. What, now, we 
may ask, is the relation of logic to the two factors 
of which all knowledge is comprised? And, first, 
what is its relation to the subject-matter of the other 
sciences? The question needs only to be asked to 
be answered ; for it is obvious, in the light of what 
has already been said, that no two departments of 
knowledge study the same material. Logic, there- 
fore, cannot study the same subject-matter as any 
other science without losing its identity by becoming 
absorbed in that science. For example, if logic were 
to study the origin, growth, and function of political 
institutions, the result would be, not a new knowl- 
edge, but an old one under a new name. Political 
science and logic would then be the same things. In 
like manner, if logic were the study of plants it 
would be identical with botany. Further illustra- 
tion is not necessary. The subject-matter of logic 
is not identical with that of any one of the other 
knowledges. What, secondly, is its relation to the 
thought factor which, as we have seen, is present 
in all knowledge? Our answer is that it is this 
thought factor in the various knowledges that logic 
makes the direct object of its study. But logic's 
relation to this thought element is different from 
that of any of the other sciences. In the several 
knowledges, thought is the means by which the 



THE PROBLEM OF LOGIC 11 

qualities and relations of objects are described and 
explained. Ordinarily, we are no more aware of its 
presence, than we are of the pane of glass through 
which we look out upon the landscape that lies out- 
side our window. But if, for any reason, we become 
curious to know how thought does its work, to find 
out whether it follows any method, we should then 
set thought before our minds as a distinct object of 
study, and the resulting knowledge would be called 
logic. That is to say, logic arises when the thought 
factor which is present in all knowledge is set before 
the mind as a subject of investigation. Thought 
then becomes the material of a special study, and the 
name of that study is logic. 

Logic as Scientia Scientarium. We have just seen 
that logic is the science that is interested in the way 
in which thought does its work in the several fields 
of knowledge. Now we have previously seen that 
we are not everywhere equally successful in system- 
atising our thoughts-about-things. Some branches 
of knowledge are more loosely, and some are more 
closely, organised. This fact we may attribute in 
part to the greater complexity of the subject-matter 
of some of the knowledges. History, for example, 
is a less exact science than is physics just in propor- 
tion to the greater complexity of the material that 
it studies, and to the difficulty of bringing its mate- 
rial under controlled observation. Now, in this con- 
nection, the question arises — Do the several depart- 
ments of knowledge equally well provide guidance 
for the formulation of logical doctrine? If some 



12 A TEXT-BOOK OF LOGIC 

branches of knowledge are better articulated than 
others, should we not expect that the former would 
illustrate the methods of thinking more perfectly 
than those branches that have not taken on the same 
degree of coordination; and, further, if we can 
find any group of knowledges that stands pre-emi- 
nent in this respect, should we not save time and 
trouble by making it the basis of our study of logical 
doctrine? Such questions have been asked, and it 
has been customary to answer them in the affirm- 
ative. Thus logicians, from the days of Aristotle 
to the present time, have expounded the subject of 
logic with their eyes on the methods adopted by the 
better articulated sciences ; and, by some, the study 
of logic has been confined to an examination of the 
methods that have proved useful in reaching the 
truth in such sciences. From this point of view, 
logic has been looked upon as a science that lies hid- 
den in the various sciences, very much as the pattern 
lies hidden in a picture puzzle. All that needs to be 
done, according to this view, is to bring logic into 
the light that it may direct the labors of future 
workers in the field of the sciences. It is in this 
sense that logic is spoken of as scientia scientiarum : 
it is the science of sciences in the sense that it under- 
lies and gives direction to all the work that science 
undertakes to do. 

The Humanistic Influence in Logic. That view of 
logic which identifies it with the study of scientific 
method has always been considered a little partial 
and extreme, and it is doubtful if Aristotle, who 



THE PROBLEM OF LOGIC 13 

was the first and greatest of the formulators of 
logical doctrine, and whose authority has been ap- 
pealed to in support of this position, would subscribe 
to it. It is probable, as Minto has shown, that in 
organising his logic, Aristotle had in mind, as much 
the formulation of the rules of dispute in the social 
life and court procedure of his times, as the 
systematisation of the methods of thought in the 
body of the scientific knowledge of his day. How- 
ever that may be, it is certain that our own times 
are witnessing a marked humanistic reaction against 
a stiff and formal view of logic, and modern logi- 
cians are looking to the less exact forms of knowl- 
edge for enlightenment as to the way in which the 
business of thought is carried on ; indeed, their study 
now extends to the ways in which difficulties arise 
and are overcome in our everyday life. This exten- 
sion of the field within which the logician pursues 
his studies cannot be taken as an evidence of indif- 
ference to a strictly logical doctrine ; rather must it 
be viewed in the light of what is taking place in other 
departments of knowledge where an investigation 
of the simpler, more primitive, forms has been found 
to elucidate much that was obscure in the more com- 
plex forms of the subject-matter studied by these 
departments. In zoology, for example, interest in 
the simpler organisms has flooded with light our 
understanding of the more complex ones, and in psy- 
chology the study of the mental processes of young 
children and of the feeble minded has added to our 
understanding of the adult, normal mind. Hence it 



14 A TEXT-BOOK OF LOGIC 

is felt that if we consider those methods of thought 
which, in some of the sciences and in the ordinary 
business of life, have not taken on a strictly rigid 
form, we shall be able to understand the nature of 
thinking in a more satisfactory manner than if we 
confined our observation to those sciences in which 
the highest degree of precision in methods had been 
attained. 

Relation of Logic to Psychology. We have used 
the term 'thought' in the foregoing pages in a some- 
what broad way. It has meant, in general, the men- 
tal factor which is never absent from the knowledge 
experience. Now the question may arise whether in 
claiming thought, in this sense, as the special sub- 
ject-matter of logic we have not confused logic with 
psychology. For what is psychology if it is not a 
study of mental processes? 

Now there are two ways in which we may dis- 
tinguish between logic and psychology. In the first 
place, we may remark that there is a quantitative 
difference between the two. Grant, for the time 
being, that the subject-matter of both these sciences 
falls within the field that we usually designate as 
mental, it may, nevertheless, be said that not all that 
is mental is included in the scope of logical inquiry. 
Logic is interested mainly, if not exclusively, in 
what are called the cognitive processes; that is, in 
those processes in and through which we either 
affirm or deny something. But cognition in the 
strict sense, cannot claim to be more than a very 
small part of one's mental life. The latter, and so 



THE PROBLEM OF LOGIC 15 

the field of psychological inquiry, includes, in addi- 
tion to knowledge or cognition, other kinds of men- 
tal processes, e. g., feelings, emotions, volitions. The 
whole field of the conscious life lies open to the in- 
vestigation of psychology; but logic is interested 
chiefly in that part of it that is called cognition, and 
in the other parts only so far as they help us to 
understand what human knowledge is. 

In the second place, we may remark that although 
logic and psychology both study the cognitive proc- 
esses, they do not study them from the same point 
of view. Psychology is satisfied when it has de- 
scribed and explained the mental changes that take 
place in a cognitive process. Logic is concerned, not 
with the natural history of cognition, but with cog- 
nition as an instrument by means of which the world 
of reality — minds and things — is understood. That 
is, the images and ideas which make up any cognitive 
process, and which psychology endeavours merely to 
describe and explain, are, from another point of 
view, taken to represent objects in the real world; 
and it seems to be the function of these images and 
ideas to place those who have them in communica- 
tion or contact with objects which exist in some sort 
of independence of these images and ideas. It is this 
character of images and ideas as affording us a 
knowledge of a world of objects that is the stand- 
point of logic, and which enables us to distinguish 
the logical from the psychological method of dealing 
with the cognitive processes. Logic is not interested 
to know what images and ideas are present in con- 



16 A TEXT-BOOK OF LOGIC 

sciousness, but whether the images and ideas that 
we entertain are true, that is, afford us accurate 
knowledge of the objects which they represent and 
to which they point. Or, to put it more succinctly, 
logic studies the conditions of the truth or falsity 
of our ideas, a problem which, for psychology, is 
quite indifferent or non-existent. 

Logic as an Art. It is sometimes said that logic is 
an art as well as a science. The meaning of this 
statement can be made clear, if we bear in mind 
that the term 'art' is used in two senses. In the 
first and most common meaning, it refers to the 
developed skill that one acquires through practice 
of a set of more or less mechanised movements. If, 
for example, you go into a machine shop and watch 
the workmen at their tasks, you will find them en- 
gaged in different activities, and displaying varying 
degrees of skill. It is this ability to do a given task 
with some degree of proficiency that we call the 
workman's art. Art is, then, a specialised ability 
to do. On the other hand, there is an ability, much 
more specialised than the mechanic's, which con- 
sists in the perception of how a task should be done, 
but which does not necessarily carry with it an 
ability to perform it. The engineer, for example, 
is able to plan and superintend building enterprises, 
although he does not have the ability of the work- 
men upon whom he must rely if these enterprises 
are to be translated into steel and brick and stone. 
The skilled workman and the engineer display two 
different orders of practical ability, and we may 



THE PROBLEM OF LOGIC 17 

speak of each one of them as possessing and prac- 
ticing an art. 

Now, when logic is spoken of as an art, it is well 
to be clear whether we are using the term art in the 
first or in the second of the two meanings just dis- 
tinguished; whether we are thinking of logic as 
giving to its students the ability to think correctly, 
or whether we are thinking of it as giving its stu- 
dents the ability to detect the correctness and incor- 
rectness of arguments. We are inclined to the 
opinion that, in the case of logic, these two meanings 
cannot be separated, and that in learning the regu- 
lative principles of logic we are at the same time 
acquiring the ability to order our thoughts in a log- 
ical manner. The reason for this opinion, briefly 
stated, is that the study of logic is and must remain 
unprofitable to anyone who, while he is studying it, 
does not practice the methods of logical thinking. 
The meaning of this statement will become clearer 
as we proceed, but it should be taken by the student 
as a suggestion that the way to gain a knowledge of 
this subject is to think each step logically as it is 
unfolded in the successive chapters. For example, 
we shall presently be speaking about terms, and we 
shall call such things as, 'the Sultan of Turkey/ 
'good/ 'H 2 S0 4 ,' 'man/ — terms. Now, it is obviously 
impossible for anyone to memorise, or even to make, 
a list of the things that logic calls terms. The only 
alternative, therefore, is for the student to acquire 
the ability to think — term, to understand what a 



18 A TEXT-BOOK OF LOGIC 

term is. When he has done this, he will have to 
employ this acquired ability in all his subsequent 
study, so that it never becomes rusty through dis- 
use. The same remark applies to all the topics of 
which logic treats. In this sense, therefore, the 
study of logic is at the same time practice in the 
methods of logic; and it is because we cannot ac- 
quire a knowledge of the correct methods of thought 
without at each step practicing these methods that 
logic may be said to be an art in both of the senses 
defined in the beginning of this section. 

What Logic is. We may now, with a summary 
of the foregoing discussion in mind, undertake a 
statement of what logic is. We have seen (1) that 
logic presupposes the existence of knowledge in one 
or more of its several forms, and that it has sus- 
tained this relation to the other knowledges from 
the very beginning. Aristotle, as we said, was 
prompted to write his treatises on logic from the 
desire that, along with the improvement in the 
sciences and arts, there should go the consciousness 
of the method by which, in these fields, conclusions 
were being reached. Logic, therefore, was not an 
invention of new instruments of research and knowl- 
edge, but the formulation and systematisation of 
those that in use had already proved their effective- 
ness. Consequently, we said (2) that when logic 
sets about its task, it distinguishes between the sub- 
ject-matter and the thought element in the knowl- 
edges, and erects the latter into a separate object 
of study. Logic, therefore, is a study of the relation 



THE PROBLEM OF LOGIC 19 

of thought to human knowledge. But, in this con- 
nection, we had to point out (3) that the interest of 
logic in thought is different from that which the 
several knowledges have in it. The knowledges aim 
to reach conclusions that increase our understanding 
of the nature of the objects they select for study. 
It is true that this increased understanding is 
reached by thinking; but, so long as results are 
reached, the scientist is no more concerned with 
thought than is a farmer with the engine that drives 
the machine that threshes his grain. This is not 
the case with logic. It studies thought with a view 
to finding out its methods of work. From this point 
of view, therefore, we may say that logic is a science 
of the methods of correct thinking. But (4) if logic 
is to be guided by the best examples, it will naturally 
be interested in the methods of the natural sciences. 
The influence of this interest of logic in the natural 
sciences has been to restrict unduly the scope of log- 
ical inquiry, and thereby to give to logic an impor- 
tance that originally did not belong to it. The 
restriction is seen in the definition of logic as a study 
of scientific method, and the new importance it thus 
assumes is expressed in its claim to be the scientia 
scientiarum, — the science that makes all the other 
sciences possible and real. In this connection, we 
pointed out (5) that this view could not claim the 
support of the earliest writers on the subject, and 
that in our own times a positive reaction against it 
has set in. The form that the reaction has taken is 
to extend the field of logical observation so as to in- 



20 A TEXT-BOOK OF LOGIC 

elude not only the more highly specialised sciences, 
such as physics and chemistry, but also those that 
are less fully developed, such as the biological, social, 
and historical sciences. From this standpoint, logic 
is a study of the methods of human knoivledge of 
whatever kind the knowledge may happen to be. In 
the section on psychology and logic we saw (6) that 
thought may be studied in two quite different ways. 
We may study thought, for example, as a series of 
consciousnesses made up of various elements and 
possessing various attributes. This is psychology. 
If, however, we study the function of thought in 
affording us a knowledge of the real world, we are 
led to a very different result, and the kind of knowl- 
edge thus reached will be logical rather than psycho- 
logical in character. For logic, that is to say, 
thought has a meaning over and above what thought 
is as an item in a stream of consciousness. What 
thought is or is like is one thing, and what thought 
means and does it another. It is from the latter 
point of view that logic studies it. If, therefore, 
meaning, as one writer says, is a "product of thought 
in its relation to reality, or of reality in relation to 
thought," logic may be defined as a science of the 
development of meaning, or, more briefly, as the 
science of meaning. 

Only one more point need be raised, namely, in 
what sense logic is a science at all. In the last sec- 
tion we saw that logic is an art in the sense that 
engineering is an art, but we also saw that as such 



THE PROBLEM OF LOGIC 21 

it is an art in a somewhat special sense. It is, if 
we may say so, an intellectual art, an art that con- 
sists in knowing how certain things should be done. 
In this respect, logic, to use Minto's illustration of 
the Aristotelian logic, may be likened to "Cavendish 
on Whist," — a book that states the rules and illus- 
trates the methods of playing the game. We have 
done ample justice to this feature of logic, and the 
student is not likely to lose sight of its importance 
as we proceed. But we now ask whether it is also, 
in any sense, a science; in the sense, for example, 
that physics and chemistry are sciences. Now we 
ought to be clear that these sciences do not exist for 
the purpose of providing rules that students may 
follow in performing laboratory experiments. If 
this were the whole extent of the scientific character 
and purpose of these subjects, they would differ in 
no respect from the practical sciences in which we 
learn how certain things are done. If, however, we 
consider these sciences more carefully we shall see 
that they aim to formulate principles or laws, and 
that it is only as the experiments enable us to ascer- 
tain these principles that they have their perfect 
work. So we may say with respect to logic. It has its 
experimental side, and it formulates rules and states 
the methods of correct thinking ; but it goes beyond 
this and tries to express the laws or the principles 
to which every concrete case of thinking actually 
conforms. In the light of this fact, we may conve- 
niently bring this chapter to an end with the state- 



22 A TEXT-BOOK OF LOGIC 

ment that logic is a study of the methods of correct 
thinking and of the principles on which these meth- 
ods are based. 

REFERENCES 

B. Bosanquet, The Essentials of Logic, Ch. I. 

J. E. Creighton, An Introductory Logic, 3d Edition, Ch. I. 
J. G. Hibben, Logic, Inductive and Deductive, Introduction I. 
S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
tion, Ch. I. 
W. Minto, Logic, Deductive and Inductive, Introduction I. 

C. Read, Logic, Deductive and Inductive, 3d Edition, Ch.. I. 

Advanced 

J. M. Baldwin, Thought and Things, Vol. I, Ch. I. 

W. R. B. Gibson, The Problem of Logic, Introduction. 

H. W. B. Joseph, An Introduction to Logic, Ch. I. 

H. Lotze, Logic, Vol. I., Introduction. 

F. C. S. Schiller, Formal Logic, Ch. I. 

C. Sigwart, Logic, Vol. I, Introduction. 

J. Welton, Manual of Logic, Vol. I., Ch. I., II. 

QUESTIONS 

1. How do the various sciences differ from one another? 
Illustrate. 

2. What function has thought in the several sciences, and 
what reason can you give for your answer? 

3. What do you understand by knowledge, and into what 
two factors may all knowledge be analysed? 

4. What is meant by calling knowledge systematic? 

5. Upon what three factors does the systematisation of 
knowledge depend? 

6. Is all knowledge equally systematic? Illustrate. 

7. What is meant by 'knowledges'? 

8. "It is the knowledges that make logic possible." Ex- 
plain. 



THE PROBLEM OF LOGIC 23 

9. What is the subject-matter of logic? What is the rela- 
tion of this subject-matter to the other sciences? 

10. What is meant by calling logic scientia scientiarum? 

11. Describe the humanistic reaction in logic, and how does 
it affect our view of the subject? 

12. In what two ways do logic and psychology differ from 
one another? 

13. What two meanings may be given to the term art? 

14. Is logic an art as well as a science? Explain. 

15. Summarise the various definitions of logic in this chap- 
ter, and state clearly the points of view from which these 
definitions are made. 

EXERCISES 

1. Point out the subject-matter in the case of any six 
subjects with which you may be acquainted. 

2. Show the relation that thought has to each of the sub- 
jects chosen for your answer to the previous question. 

3. Cite concrete instances of the way that thought be- 
comes a problem in the pursuit of various kinds of 
knowledge. 

4. Illustrate how observation of the ordinary modes of 
conversation may advance our knowledge of the log- 
ical processes. 

5. Use concrete examples to show the limitations to which 
logic would be subject if it confined itself to the study 
of the scientific mind. 

6. Give instances of the practical value that is claimed for 
an acquaintance with logical doctrine. 



CHAPTER II 

THE JUDGMENT 

The Meaning of Thought. Before carrying our 
study of the logical character of the thought proc- 
esses, begun in the last chapter, into greater detail, 
we wish to call attention to two simple and obvious 
considerations. In the first place, we may observe 
that the objects that come before us in the course 
of our experience present a great variety of charac- 
teristics. The object of which we are aware may 
be part of the material world, — the starry heavens ; 
it may be part of the common human life that today 
we share with our fellows, — the rush of the ambu- 
lance in its race with death; it may be part of the 
inner individual life, — the secret and incommuni- 
cable thing that a man sees when he sits down face 
to face with himself. In short, the object may be 
anything from "the choir of heaven to the furniture 
of earth;" but whatever it is, it is an object because, 
and in so far as, we have experience of it. We shall 
use the term object, then, to denote that of which 
we have experience, without respect to the kind of 
object it is, or the kind of experience in and through 
which it may be said to exist. But this leads to a 
second remark. There are, as we intimated just 
now, a variety of ways in which we experience, or 
react to, or are aware of objects. The terms per- 
ception, memory, imagination, feeling, volition, are 

(24) 



THE JUDGMENT 25 

the names of some of the more familiar ways of 
reacting to objects. Thus we may perceive an 
object, or remember it, or imagine it, or be affected 
pleasantly or unpleasantly by it, or do something 
because of it. All these are, of course, familiar 
experiences, and we do not need to be psychologists 
to be aware of the fact that the object assumes a 
somewhat different character for the different activ- 
ities through which it is experienced. That is to 
say, the object as we perceive it, or remember it, 
or imagine it, or are pleasantly or unpleasantly 
affected by it, or do something because of it, has a 
slightly altered aspect in these several modes of 
reacting to it. 

Now it will probably help us to understand the 
problems of this chapter if, at the outset, we observe 
that the recognition of this implication of objects 
in all or most of our conscious processes has led to 
a certain looseness in our use of the term thought. 
By some, especially among the psychologists, thought 
is the name that has been employed to denote the 
various kinds of mental processes, — perception, 
imagination, feeling, desire, emotion, etc. James, 
for example, speaks of the 'stream of thought,' a 
phrase in which the term thought, as he tells us, is 
used for "every form of consciousness indiscrim- 
inately." In a somewhat more restricted sense, the 
term thought or cognition is used, in distinction 
from feeling and conation or striving, with which 
it is intimately associated, as the name for one of 
the ultimate modes of consciousness. It appears in 



26 A TEXT-BOOK OF LOGIC 

this sense in the writings of Stout and Ladd. When 
employed with this meaning, it denotes all those 
mental activities, such as perception, memory, con- 
ception, etc., in which we are, in one way or another, 
concerned with the nature of objects. "It covers," 
as Stout says, "all modes and degrees of being aware 
of or cognisant of an object." A still more special- 
ised use of the term is that which limits its appli- 
cation to those processes whereby we designate 
objects merely as the objects that are, at the present 
moment, under consideration. To think, to use 
James' definition of conception, with which the term 
thought in this sense is practically synonymous, is 
to "identify a numerically distinct and permanent 
subject of discourse;" to mark it off from other 
objects, and to make it the bearer of whatever attri- 
butes or relations that our 'thoughts-about' it may 
show that it actually possesses. 

The three meanings just distinguished of the 
term thought are doubtless closely connected from 
the psychological point of view. For if psychology 
be regarded as "the science of the processes whereby 
an individual becomes aware of a world of objects 
and adjusts his actions accordingly," and it is so 
regarded by Stout, it is perfectly obvious that the 
several mental processes must be viewed, in them- 
selves and in their relations to one another, as modes 
of conscious activity which further, more or less 
directly, that acquaintance with objects which all 
the three statements of the meaning of thought 
alike emphasise. We need not consider whether, 



THE JUDGMENT 27 

and, if so, in what sense all the fundamental mental 
processes serve the purpose of establishing and im- 
proving our acquaintance with things ; whether, for 
example, the so-called affective processes are cor- 
rectly interpreted in this way. It will be enough 
if we recognise that certain processes can be grouped 
together, and can be regarded as having for their 
distinctive function the discriminating and relating 
of the objects of experience. If we approach the 
problem of thought from this point of view, we see 
that the term thought, in the second and third mean- 
ings distinguished above, have a peculiarly close 
relation. According to the second meaning, thought 
is a continuous process which, beginning in percep- 
tion, culminates in what the psychologist calls judg- 
ment and reasoning. Without denying that thought 
is dependent upon the more elementary processes of 
perception, the third meaning limits the application 
of the term to the later processes in which, more 
particularly, we acquire what was described in the 
previous chapter as 'knowledge-about' objects. For 
the one, thinking is the name for a process in which 
perception, memory, imagination, conception and 
judgment may be found to function; for the other, 
it is a name by which conception and judgment are 
specifically signified. In whichever of these two 
contrasted senses the term is used, each implies, 
what is undoubtedly the fact, that there is no unique 
faculty of thought, that thought is a complex process 
in which a number of mental activities combine to 
give us a knowledge of objects, and that, while some 



28 A TEXT-BOOK OF LOGIC 

of these activities enable us to identify distinct and 
permanent subjects of discourse, others carry us 
beyond this to the knowledge of a system of existing 
things in which numerous terms and relations are 
discernible. 

Judgment and Thought. Now when we consider 
the subject of thought from the standpoint of logic, 
it is in the third of the meanings already distin- 
guished that, in the main, we shall use the term. 
Thought will thus signify the processes of judgment 
and reasoning, those processes in which the cogni- 
tive process as a whole culminates. Logic, that is 
to say, is particularly interested in the terminus 
ad quern of the thought-process, in the goal toward 
which our desire for knowledge points; and it 
studies the process of reaching the goal only when 
a knowledge of such process enables it to determine 
the nature and grounds of the validity that is 
claimed for thought. Thinking thus comes to be 
regarded by logic as having a character which is 
liable to escape notice so long as we keep strictly to 
the psychological point of view, — the character of 
assertion. And in order to give prominence to this 
feature of thought, logicians are more apt to speak 
of judgment than they are of thought. Thinking, 
as we have seen, is a mental process in which the 
psychologist distinguishes a number of constitutive 
processes, — perception, memory, etc. Judgment, 
as it is used by the logician, regards the thought 
process as being concerned with the specification 
of a content, the assertion of which is logically the 



THE JUDGMENT 29 

characteristic thing about a judgment. The content 
of the thought process is taken up by the judgment 
and constituted the subject-matter of assertion. 
Thus the experience, say, of red calls from the psy- 
chologist the statement that, like all sensational 
experiences red cannot be described, but must be 
experienced if any one is to know what the word 
signifies, that it is produced by the action, on the 
rods and cones of the retina, of ether waves of a 
certain length, and that these changes are continued, 
by way of the optic nerve, in a manner that is little 
understood, to the occipital lobe which is the cortical 
centre of the visual consciousness. For the logician, 
the particular patch of colour called red merely 
exists, and the acknowledgment of it as existing, 
by the individual who experiences it, is what is 
meant by assertion or judgment. The red is the 
content of the processes which are described by the 
psychologist, and it is this content that is asserted 
as the subject-matter of the judgment. Whatever, 
then, exists as content of thought, may become the 
subject-matter of a judgment; and we may, there- 
fore, define a judgment, broadly, as an assertion of 
the qualities and relations of the object of thought. 
A word or two may be necessary at this point 
to guard against a possible misunderstanding of 
what is meant by assertion as the central fact of 
the logical judgment. In current usage, to assert 
means to express in words the thoughts and opin- 
ions that we entertain about things. It is commonly 
employed as the equivalent of 'to say something.' 



30 A TEXT-BOOK OF LOGIC 

In logic, assertion has nothing to do with speech. 
We may, of course, express what we assert, but 
we can assert without putting into words, or into 
any other set of social symbols, the qualities and 
relations of the object of thought. The question we 
are now considering, moreover, has nothing to do 
with the problem whether, as individuals, we can 
think without words. It is a simpler matter than 
that; and all that we say is that no one, merely 
because he judges, is bound, in order to give his 
judgment the character of assertion, to put into 
language the truth or fact that his judgment em- 
bodies. On the contrary, by assertion we mean the 
attitude of mind in which, for that mind itself, 
there consciously exists such an acquaintance with 
an object that, in itself and its relations, it is dis- 
tinguished from other objects with which it occurs 
in a common field of knowledge. For example, I 
may be looking over a collection of curiosities that 
a friend has accumulated from the four corners of 
the earth. I look at the objects one after the other, 
and find that each is a strange and unintelligible 
thing, and, as I put it back into its place, it is soon 
lost in the mass of the other strange and unintel- 
ligible things. If, however, I should find in the col- 
lection an object that is familiar, there would be, 
under the circumstances supposed, a mental tang 
and 'feel' toward it that would make it, as I put 
it, too, back in its place, stand out from the rest, — 
its identity would not get lost in the multitude of 
strange things. What makes the difference in this 



THE JUDGMENT 31 

case is my mental attitude toward it, — a mental 
attitude that, in this instance, is called recognitive 
judgment. In logic, the mental attitude in which 
we find the characteristic feature of the judgment 
is described as assertion. Whenever we judge we 
assert, and whenever we assert we put marks upon 
the objects that come before us by which they attain 
unique distinction. 

Other Mental Attitudes Akin to Judgment. It may 
help to emphasise the assertive character of the 
judgment if we distinguish certain other attitudes 
which, like assertion, have received, in the develop- 
ment of language, definite verbal forms. Judgments, 
it should be observed, are always expressed in the 
indicative mood, and what they assert is always true 
or false. On the other hand, interrogatives, imper- 
atives, optatives, and exclamations do not assert, 
and therefore are not judgments, but express either 
an inquiry, a command, a wish, or an emotion. Of 
the wishes that optatives express we can say that 
they are reasonable or unreasonable. The com- 
mands of imperatives can only be obeyed or dis- 
obeyed. Our interrogatives formulate inquiries and 
call for an answer. Exclamations are word ges- 
tures that express our emotional attitudes toward 
situations. But while interrogatives, imperatives, 
optatives, and exclamations are not judgments, they 
imply attitudes of mind which, if asserted, would 
be judgments. The rhetorical question, 'Is thy ser- 
vant a dog?' doubtless implies an assertion, and is 
equivalent to Thy servant is not a dog.' But not 



32 A TEXT-BOOK OF LOGIC 

only the rhetorical, but any question may be inter- 
preted in a similar way. For to ask a question 
would be meaningless unless we thereby implied 
that something can be asserted of its subject, and 
it is to this something that the question, in a general 
way, points. If, for example, I ask, 'Is that a fire?' 
I imply that it is a fire, but not in the way that 
would warrant me in asserting it as a fact. With 
imperatives the case is different. 'Come,' 'Do this,' 
cannot be said to be either true or false, and they 
imply assertion only if imperatives are indicated 
actions that have reference to a situation which 
they either help or hinder. Imperatives, that is, get 
their meaning from a context that exists in the 
mind of the person issuing the command, a context 
which must rely for its development upon the action 
of the person to whom the command is addressed. 
The implied judgment, therefore, may be thrown 
into the hypothetical form thus: 'If you do the 
thing commanded, such and such things will happen.' 
Commands, that is, are abbreviated antecedents of 
hypothetical judgments. Optatives express a desire 
for some state or condition which is thought of as 
possible, though not, at the moment the wish is 
entertained, as actual. They imply the assertion 
of definite objects as the objects of desire. In this 
way we must interpret, for example, 'Would that I 
were dead!' It implies that 'to be dead at this 
moment' is really a desired object. Such exclama- 
tions as 'Absurd!' 'Impossible!' are predicates of 
implied judgments, and by them, besides expressing 



THE JUDGMENT 33 

our personal attitudes, we are also characterising 
situations. 

Judgment and Groundless Statements. Before 

proceeding to develop other features of the judg- 
ment, as this has been defined in the previous sec- 
tions, there is a class of statements about which we 
are called upon to say something if only for the 
sake of clearing our exposition of the subject under 
discussion from unnecessary ambiguity. We have 
seen that assertion is the main characteristic of 
judgment, and that what a judgment asserts is some 
quality or relation of the objects about which we 
think. It would seem quite obvious, therefore, that 
unless we think about some object or other, there 
can be, for us, no such thing as judgment. Judg- 
ment implies thought, and thought implies some- 
thing thought about. 

In contrast to judgment, as thus understood, we 
are confronted with a class of statements which 
simulate judgments, but which fall short of being 
true judgments because they are not based on the 
thinking of the person who makes them. We may 
cite in illustration not only the parrot-like state- 
ments of the class-room recitation, but the ill- 
informed and often misleading expressions of opin- 
ion that many of us allow ourselves to make with 
confidence on all sorts of subjects about which we 
know relevantly nothing. The certainty that at- 
taches to such statements has little or nothing to do 
with their subject-matter; it usually rests upon the 



34 A TEXT-BOOK OF LOGIC 

confidence we have in 'authority' of some kind or 
other. For instance, students rarely call in question 
the statements they find in their text-books, and 
consequently they are ready to state as true any- 
thing they read in them for no better reason than 
that it is 'in the book.' Indeed, most of us entertain, 
and express to others, beliefs that are based solely 
upon statements we have read in some magazine or 
newspaper, or have heard in a public address or in 
private conversation. To communicate, in this way, 
the opinions of others is doubtless a valuable social 
function, but the statements in which another's 
views are given currency should not be confused 
with judgments in the sense in which this term has 
been defined. We may, for want of a better word, 
distinguish these statements as groundless asser- 
tions, for what enables us to distinguish them from 
true judgments is the fact that, in respect of the 
latter, we are always more or less conscious of the 
reasons for what the judgment asserts. Our judg- 
ments are, as it is said, grounded judgments, and 
the grounds of the judgment are the reasons that 
thought can give for the particulars asserted by the 
judgment. For, as we have seen, the asserted par- 
ticulars are always what thought reveals as true of 
the subject thought about. 

The distinction that we have drawn in this sec- 
tion between groundless statements and judgment 
corresponds, in a general way, to that which appears 
in the history of Greek speculation as the distinction 
between 'opinion' and 'knowledge.' 



THE JUDGMENT 35 

Practical and Theoretical Aspects of Thought. 
Whether we use the term thought in the broadest 
of the meanings already distinguished, or in one of 
its more restricted senses, it is undoubtedly true 
that we cannot fully describe the experience that 
the term denotes without recognising the fact that, 
along with those differentiations which the object 
of thought undergoes, for example, in perception, 
in ideal representation, and in ideational thought, 
tendencies of a practical sort are aroused which not 
only accompany the thinking process, but, in part, 
give it the character and direction which it undoubt- 
edly possesses. Thus the psychologists have been 
accustomed . to recognise that instinctive impulses 
are present in perception which tend to place the 
percipient subject in relation to external objects; 
that in ideal representation active tendencies of the 
kind called desires are directed toward objects 
which, not being actually present, are held before 
consciousness as an end to be realised; and that in 
ideational thought the process of generalisation for- 
mulates ideals which are sometimes of so complex 
a character that, while they may become the objects 
of individual desire,, they are attainable only as the 
result of social cooperation. Whether, therefore, in 
its simpler or more complex forms, thought seems 
to have, not only an aspect which is directly con- 
cerned with the definition of an object, a theoretical 
aspect, but also a practical aspect, a certain conative 
tendency whose function it is to direct the process 



36 A TEXT-BOOK OF LOGIC 

of thinking and to give its content a definite charac- 
ter and objective. 

Relevant Assertion. From the point of view we 
have now reached, we may indicate certain features 
of the logical judgment which correspond, in, a gen- 
eral way, to this distinction in the nature of think- 
ing itself. The function of judgment we have said 
is assertion. We have now to point out that when- 
ever assertion satisfies the logical conditions of 
truth, and is not mere or groundless assertion, it is 
seen to have two characteristics both of which are 
included under the single term 'relevant.' More 
explicitly stated, judgments, in the logical sense of 
that term, are always relevant assertions, and their 
relevancy is based upon, and is the logical expression 
of, the theoretical and practical aspects of the 
though process which were indicated above. Judg- 
ments, in other words, always refer to some object, 
and fulfill some need of the person asserting the 
judgment. Whenever they do either or both of these 
things, our judgments are said to be relevant asser- 
tions. Briefly stated, judgments are assertions that 
are relevant (1) to the motives that operate to 
produce them, and (2) to the material by which 
they are called forth and to which they refer. 

To consider the first meaning of relevancy, that 
which refers to the motives that operate to produce 
our judgments, we may say that this is concerned 
with the reasons why any one judges at all. If, 
then, it were asked why any one judges, the answer 
would be that one cannot 'get along' without it. In 



THE JUDGMENT 37 

a broad way, the life of thought is based in and 
grows out of our practical needs. As an illustration 
of what this statement means, we may refer to the 
development of agriculture in the history of civil- 
isation. Before agriculture had become one of the 
institutions of human society, men no doubt were 
confronted with the problem of food supply, and 
they met this problem in a way that was fairly 
satisfactory until the accumulation of various forms 
of wealth made a predatory and wandering life both 
irksome and unprofitable. When, for instance, the 
domestication of animals had become an accom- 
plished fact, this not only made a wandering life 
more difficult, but it also exposed the primitive com- 
munity to greater loss through drought, long jour- 
neys, and marauding attacks from hostile and mer- 
cenary tribes. But unless fruits and cereals could 
be domesticated, as animals had been, there was 
before the primitive community the necessity of 
seeking food where it grew, whatever the risks and 
losses that might be incurred. Now it takes but a 
little imagination to see that the great difficulties 
that beset tribes advancing from a wandering to a 
settled mode of life would act as a stimulus to their 
thought, and would engage their thought in the 
direction of these difficulties themselves. It may 
seem to us who have grown up under settled con- 
ditions of life a simple matter to perceive the prob- 
lem and the solution of which it was capable. But 
before the food supply of man and beast could be 
raised, within a restricted area, by man's efforts 



38 A TEXT-BOOK OF LOGIC 

from seeds, there was required exactly that develop- 
ment of the thought processes which the mainte- 
nance of the institution of agriculture calls for at 
the present day. What, therefore, we may say is 
that the principle of this illustration, namely, that 
our needs stimulate the judging activity and direct 
it toward an understanding of whatever threatens 
the satisfaction of these needs, is capable of indefi- 
nite extension ; and that the incentives to knowledge 
become more numerous and diverse as, with the 
growth in complexity of our social life, obstacles 
are multiplied, and needs increase in number or 
change their form. Thus, over the whole course 
of our experience, thought not only interprets the 
environment, but determines the particular adjust- 
ments that, under change of environment, are neces- 
sary if the varying needs of life are to be met. 

The relevancy of our judgments to the varying 
needs by which they are called forth may be further 
illustrated, and, for this purpose, let us suppose 
that we have a hundred books, and that our problem 
is what we are going to do with them. It is very 
probable, first, that we shall want to have them all 
in one place. Within the space allotted to them, we 
are likely to arrange them under some scheme of 
classification, — authors, subjects, or what not. 
Now why do we do this? Is it needless? By no 
means. We are simply obeying in our manner of 
dealing with the books a fundamental need for 
order. But what particular order we impose upon 
the books will depend upon the particular form that 



THE JUDGMENT 39 

the demand assumes. Thus, in the first instance, 
we bring all the books together in one place; place 
is the principle of our classification. In the second 
instance, we have carried the matter further, 'and 
have arranged the books, let us say, according to 
subjects, — subject-matter is a more specialised 
form of the need for order which operates through- 
out all our classifications. But if it is asked why 
any order is necessary, we can only say that when 
classified objects are more easily handled and used. 
The point of the illustration is that, when we have 
to deal with a hundred books, we are bound to think 
about the books in terms of our interest in them. 
Thus the first classification according to place might 
be satisfactory to the housekeeper whose interest in 
the books is aesthetic, — as articles of furniture in a 
room. The classification according to author would 
satisfy the interests of the man whose manner of 
speaking about books is, 'Oh, yes, I have Dickens, 
Eliot, Thackeray, etc.' The scholar's interest is 
most likely to be met by the arrangement according 
to subjects. In each case, what we think about the 
books, — whether as articles of furniture, or as the 
works of such and such authors, or as dealing with 
given subjects, — depends upon the interest we have 
in them. And what is true in this particular in- 
stance is true in every case of judgment. Our judg- 
ments, in a word, are assertions that are relevant 
to the interests out of which they are born. 

The foregoing statement and illustrations of the 
conditions under which the judging activity comes 



40 A TEXT-BOOK OF LOGIC 

into play indicate clearly enough what is meant by 
the practical nature of all our thinking. But be- 
cause the word practical is, in ordinary speech, so 
intimately associated with the getting of material 
goods, or with the removal of material hindrances, 
the exact meaning of the statement that all judgment 
is conditioned by the presence of practical needs is 
liable to be given too narrow an interpretation. By 
a practical need, it is true, we mean one that is con- 
cerned with getting an anticipated good, or witn 
removing a present hindrance to further goods. 
But the goods in question need not be material, and 
in many cases are not material. We have no wish 
to deny that man is an economic animal, and that 
what we call property is based in and grows out of 
his need for 'things.' But it is no less true that 
man is a social animal, and that the various organ- 
isations in which he is associated, — the family, the 
shop, the club, etc., — have their foundation in the 
needs which prompt men to associate with their 
kind. The social is, no less than the economic, a 
practical need. A similar line of remark applies also 
to our science, art, and religion. There are, doubt- 
less, intellectual, emotional, and volitional needs, 
complex in their nature, and variously combined in 
the instances just given, which impel men to seek 
their satisfaction in the formulation of the objects 
to which these needs point. Over the whole range 
of life, then, situations are constantly arising in 
which unsatisfied demands impel us to think, z. 
to think with reference to these demands. Nowhere 



THE JUDGMENT 41 

can this practical aspect of the judging activity find 
more or more pertinent illustration than in a study 
of the ways m which the human race has advanced 
in the arts of civilised life. But to bring the truth 
of this view home to ourselves, we need only to ask 
if we, as individuals, ever think when the situations 
in which we find ourselves are entirely satisfactory. 
Even a student, very often, will not think until a 
failure stares him in the face. 

Turning now to the second meaning of relevancy, 
we may say that judgments are assertions about 
the material by which they are called forth and to 
which they refer. In the development of knowledge, 
our interests never become so one-sided that our 
judgments are freed from the control of the mate- 
rial through which these interests are to receive 
their satisfaction. If, for instance, we were con- 
scious of nothing but compelling interests, be those 
interests psychologically never so definite, or if we 
were moved by a vague catholicity of mind that 
went out to everything in general, but took hold on 
nothing in particular, judgment would be impos- 
sible. There are states of mind that correspond 
more or less closely to those just described, states 
that are definite as to interests but indefinite, vague, 
or empty as to their objects; and others that are 
vague and indefinite in both respects; but no one 
would think of calling these states cognition, or the 
reactions they may involve judgments. What we 
aim at in the judgment is to characterise an 



42 A TEXT-BOOK OF LOGIC 

object in such a way that it becomes better 
known. The study of the judgment, therefore, is 
a study of the relation of thought to its object. 
Now, when one attempts to study the relation in 
which thought stands to its object, one is partic- 
ularly prone to two kinds of error. In the first 
place, he is apt to think of the mind as a passive 
mirror that reflects indifferently whatever is held 
up before it. That is to say, he is liable to overlook 
the presence in all knowledge of the interest factor 
of which we have already spoken. If, however, he 
escapes this pitfall, he is prone to go to the other 
extreme and think of the mind as a magic mirror 
that transforms out of all likeness to their own 
nature the objects that pass in front of it. That is 
to say, he is liable to overlook or underestimate the 
material factor to which attention is now being 
directed. Interests, as we have seen, do make our 
judgments significant; but if they are to reach truth 
they must also be brought under the control of 
objective fact. No judgment can be regarded as 
having reached truth which does not open to us the 
nature of the object about which it undertakes to 
inform us. The fact, therefore, about the judgment 
is that, within the sphere of the interests that 
stimulate the judging process, the character of 
our assertions is limited by the nature of the mate- 
rial or subject with which we are dealing. For 
example, in writing this section of logic, I am 
prompted by the desire to write in such a way that 
the student who reads shall be able, with ordinary 



THE JUDGMENT 43 

attention, to understand the doctrine. But what 
the doctrine is does not depend upon this interest; 
what I say must be true of the subject we are dis- 
cussing. However, this must be said, that what I 
include and what I omit, what form the sentences 
take, and what illustrations are used, are deter- 
mined by the purpose and needs the section is in- 
tended to serve. I cannot say anything I please 
about the judgment, but I can examine it to see 
how far it lends itself to the satisfaction of the 
interests that lead me to write about it. We may 
take any other illustration we please, and the same 
thing will be found true. The difference, for ex- 
ample, between history and romance, other things 
being equal, is the difference between the way the 
historian and the novelist feel themselves bound by 
the character and order of the occurrences which 
they narrate. The historian's purpose is to describe 
a complex social situation as it actually existed, and 
to develop the consequences, in the way of cause and 
effect, of the situation thus depicted. The novelist's 
treatment of the same material is much freer from 
the control of the objective events within which, as 
in a framework, his romance is made to move. But 
it is only in the former of these two cases that truth 
is the aim; the relative unimportance of this aim 
in the novel accounts for the looser handling of the 
historical material. We may, therefore, conclude 
that interest or purpose sustains and directs the 
whole process in which our judgments are formed, 
and that what the judgment asserts, since all judg- 



44 A TEXT-BOOK OF LOGIC 

ments claim to be true, must derive its character 
from the material which constitutes the subject- 
matter of the process of judgment. 

The Interest Factor in Knowledge. In the pre- 
ceding section, we have seen that judgments are 
assertions that are relevant to the interests or pur- 
pose of the person who judges, and also to the 
material or body of facts which, in the judgment, 
receive a particular characterisation. Now it will 
serve to further emphasise this distinction, if we 
call attention more particularly to the way in which 
these factors of knowledge are related to one an- 
other. We may in general distinguish two cases. 
There is first the case in which our interest in the 
objects which we are led to observe is extrinsic to 
the objects themselves, and, secondly, the case in 
which it is primarily intrinsic. 

To consider the former case, we may remark 
that we are often led to observe and make asser- 
tions about objects, not because of any particular 
interest in the objects themselves, but because of 
the relation in which these objects stand to other 
objects in which we are interested. Let us take 
as an example my observation of the shape, colour, 
and arrangement of the roses in the vase that stands 
upon the table at which I write. It is true, of 
course, that I may be induced to observe them, and 
to study their particular characteristics by reason 
of an interest that is rooted in my knowledge of 
floriculture. But, on the other hand, the attention 
that I give to the flowers may be due, for example, 



THE JUDGMENT 45 

to my interest in the person who picked them and 
placed them where, as I now write, they become 
the object of my perception. Or, if this is not the 
fact, my interest may grow out of my liking for a 
patch of colour of any kind, or for the particular 
combination of colours that the flowers present. In 
the former of these suppositions, the interest is 
social, and in the latter, it is aesthetic. In in- 
stances like these, we may say that the object 
sustains an interest that is extrinsic to itself, and 
gives to the interest a longer life than it would 
otherwise have. If, from this point of view, we 
speak of the flowers at all we should say that they 
were pretty, — a judgment it is true, but one which 
expresses one's feelings for the flowers rather than 
one which tells anything about the flowers them- 
selves. Such judgments are usually called value 
judgments, — judgments which express the value 
or worth of the objects for the individual expressing 
the judgment. We express multitudes of such judg- 
ments in the course of our lives, and of a great deal 
that is noblest and best in our experience we can 
speak in no other way. The student will find that 
most of the judgments that he expresses on morals, 
art, and religion are what are called value judg- 
ments ; judgments, that is to say, that are stimulated 
by interests that are extrinsic to the objects about 
which he judges. 

If, now, we consider knowledge in the more 
scientific meaning of the term, we shall find that 
here the interest factor is intrinsic, that it is 



46 A TEXT-BOOK OF LOGIC 

grounded in the object in a way we have seen not 
to be the fact in the class of cases just studied. 
Scientific interest, in other words, is an interest in 
objects for their own sake. Of course, it is some- 
times said that interest or purpose is altogether 
absent from our scientific activities, and that it is 
this fact that distinguishes science from all other 
kinds of knowledge. If all that has been written 
about the disinterested nature of scientific study 
were true, science would have been destroyed, before 
this, at the hands of its friends. The fact is, how- 
ever, as our study of the nature of knowledge has 
shown, there is no knowledge which does not spring 
from some form of human interest. It is not true, 
therefore, that what we mean by science, in con- 
tradistinction to what is not science, can be stated 
in terms of its freedom from interests which 
direct the course and prescribe the goal that science 
aims to reach. What is true, on the negative side, 
is that certain kinds of interests are detrimental 
to the existence of science. But to deny the useful- 
ness of certain kinds of interest, is certainly a very 
different matter from denying all interest whatever. 
For science, as was pointed out by Plato and Aris- 
totle, would have no existence were it not for that 
curiosity and wonder which is awakened very early 
in all of us by the changing appearances in the 
course of nature. It is this curiosity which, when 
specialised, is the source of scientific interest, and 
which, in its developed form, is an interest which 
centres in the objects which it prompts us to study. 



THE JUDGMENT 47 

In other words, the interest which is the motive of 
scientific effort appears in the form of a desire to 
comprehend the nature and relations of the objects 
of our experience. The better we understand these 
objects, the more alive does our interest in them 
become; and the more alert this interest, the more 
keen do we become in our study of these objects. 
The interest and the object of scientific work are 
thus keyed to each other in a way that makes them 
mutually supporting; and the further we study 
their relations, the clearer does it become, as was 
intimated above, that they are different aspects of 
a single process. Scientific interest, then, is an 
interest in objects for their own sake; it is an in- 
terest that prompts us to ascertain all that can be 
truly known about these objects. 

The Object of Judgment. If we now pass from 
the study of the relations of interest and subject- 
matter upon which we have been dwelling, and 
regard the judgment as an assertion about its 
subject-matter, certain other features of the judg- 
ment come into view. In our previous discussions, 
we have had occasion to specify what is meant by 
the subject-matter of the judgment, and this, it will 
be remembered, was found to be identical with what, 
from the psychological point of view, is denominated 
the content of thought. Thought and judgment are 
thought and judgment about some thing. Without, 
therefore, the challenge of some thing neither 
thought nor judgment takes place. But while 
thought and judgment imply the existence of a 



48 A TEXT-BOOK OF LOGIC 

subject, neither, in the strict sense of these terms, 
is identical with the existence of its subject. There 
seems to be, therefore, some other feature of the 
judgment which distinguishes it from mere aware- 
ness, and it is this feature that we have now to 
consider. 

We may perhaps bring the question of discussion 
distinctly forward by the aid of an illustration. 
Let it, therefore, be supposed that I am gazing out 
of the window while thinking about the distinction, 
within the logical judgment, that it is now my desire 
to state. I turn the subject about which I am 
thinking this way and that, experimenting with it 
until my interest in it begins to wane. What I 
find, under the supposed conditions, is that the 
more interest in the original subject wanes, the 
more insistently do factors from other parts of my 
environment obtrude on consciousness; and by and 
by I find myself wholly engaged with some of these, 
— the sloping hill side, the frozen lake, and the 
lively company of girls and boys skating upon its 
surface. In such an experience, what one observes 
is that not only has there been a change from one 
subject to another, from a logical problem to a 
physical object, but also that changes of another 
kind have accompanied those already indicated. The 
two consecutive contents of the thought processes, 
that is to say, have been followed by changes in the 
character of what, in each instance, is asserted. I 
do not find, in other words, that what I am thinking 
when engaged with the logical problem fits in with, 



THE JUDGMENT 49 

or can be carried over to, the scene in the distance 
which has now become the content of my thought. 
Each content has its own appropriate set of asser- 
tions. 'To assert of its subject significant qualities 
and relations is what we understand to' be the 
object of the logical judgment. It will serve to 
emphasise the distinction between the subject and 
the object of judgment if we recall that Bradley 
discriminates in the judgment between what he calls 
the 'that' and the 'what.' By the 'that' of a judg- 
ment we may mean the content or material of a 
thought process, that is, the subject of the judgment 
as we have used that term. By the 'what' may be 
understood the complex asserted by the judgment. 
For instance, the joyful scene upon the frozen lake, 
of an illustration already used, is the subject-matter 
of any judgment that I may make about it. In 
Bradley's terminology, it is the 'that' of the judg- 
ment. If, however, I assert that there is danger 
from the ice because of a thaw, and the children 
should be warned, this would be the object or the 
'what' of the judgment, the complex whole that it 
is the business of the judgment to assert. 

More recently a similar distinction has been 
drawn by the Austrian psychologist, Meinong. 
Meinong insists that we must not confuse in any 
act of judgment that concerning which we judge, 
and what we judge about it. The distinction that 
is thus drawn for all judgments is that with which 
we are familiar in the case particularly of legal 



50 A TEXT-BOOK OF LOGIC 

judgments. Let us say that a person is accused of 
a crime. In such a case, we may ask, What is it 
that the judge and jury are expected to judge? In 
one sense, the object of their judgment is the 
prisoner, and in another, it is, let us say, that he 
is not guilty of the offense with which he is charged. 
There seems, then, to be two objects of judgment, 
and, as this inevitably leads to confusion, Meinong 
thinks it important that they should be clearly dis- 
tinguished. For that purpose, he proposes to use 
the term 'object' to denote what we have described 
as the subject-matter of the judgment, that is, in 
the case supposed, the prisoner; and the term 
'objective' to denote what we have called the object, 
that is, in the case supposed, the verdict of the 
judge and jury. Now Meinong is perfectly right 
in saying that the object peculiar to the judgment 
is what he calls the 'objective,' that the judgment 
exists for the purpose of asserting something about 
a definitely apprehended subject-matter, and he is 
also right in calling attention to the importance of 
fixing this distinction in an appropriate terminology, 
because, in the absence of such terminology, of the 
tendency to confuse the two kinds of objects. 

The Universe of Discourse. In view of the course 
that our discussion has taken up to this point, the 
logical judgment may be defined as an assertion of, 
or of something about, the objects of our experience. 
We may, for example, assert that so and so is the 
object of which, at the time the assertion is made, 
we are thinking, or we may assert certain other 



THE JUDGMENT 51 

things, besides its existence, of such an object. In 
each of these cases there is judgment because the 
object is apprehended as having a particular char- 
acter, of existence or something else. The judg- 
ment, consequently, always implies a relational 
content of some sort, that is, an object qualified in 
a particular way, and it is such relational contents, 
as we have seen, that it is the specific aim of the 
judgment to ascertain and assert. If, for example, 
the words 'dog,' 'automobile,' 'zeppelin,' are not mere 
sounds, but significant terms, they must mean some- 
thing more than they express ; either that something 
not specified is 'dog,' 'automobile,' 'zeppelin ;' or that 
the objects denoted by these terms exist ; or that they 
have characteristics which distinguish them from 
all other objects ; or that they stand in an indefinite 
number of relations to each other, and to numerous 
other objects. Each of these alternatives illustrates 
the peculiar character of the judgment, since each 
of them specifies a content of thought in which 
relations of some sort are involved. The special 
object of the judgment, as we have seen, is to 
assert just such relational contents as these. 

The question may now be raised whether this is 
the whole story of the judgment, whether, that is, 
the asserted content embodies the whole meaning 
of an act of judgment. To this a negative reply 
must be given. Such an answer is necessitated in 
part by the fact, as we have seen, that our concrete 
acts of judgment are not satisfied with the assertion 
of any content, but only with those that are ger- 



52 A TEXT-BOOK OF LOGIC 

mane to the motives by which the acts of judgment 
are controlled. But the negative answer is ren- 
dered necessary also by the fact that the subject 
qualified in the judgment, distinguished as the log- 
ical subject, is only a part of the actual subject, 
distinguished as the real subject, which the judg- 
ment, taken as a whole, is understood to qualify. 
If this is true, a judgment asserts only part of what 
it means, and we must understand that the unas- 
serted part of its content is related to the judgment 
as the judgment's presupposition. On this view, 
every judgment must be presumed to involve or 
presuppose, besides and as part of what it asserts, 
a wider range of fact in the light of which the 
particulars which form the content of the judg- 
ment's assertion are to be interpreted. The range 
of fact presupposed by any of our judgments is 
described in logic as a universe of discourse. 

The meaning and truth of this statement will be 
readily seen in a simple illustration. Any proposi- 
tion which contains, for example, the term 'style' 
is at once recognised to mean one thing if the topic 
of conversation is current modes of dress, and that 
when the topic of conversation is literature it means 
something quite different. Thus, if we take the fa- 
miliar saying, Le style c'est Vhomme, in abstraction 
from all contexts, its meaning is certainly ambig- 
uous ; and the only hope of removing this ambiguity 
is to restore the saying to a context in relation to 
which it can be significantly asserted. Or, to borrow 
an illustration from Major in discussing a closely 



THE JUDGMENT 53 

related topic from the psychological point of view, 
we may say that "if one is engaged with astronom- 
ical matters, the word 'star' means a heavenly body. 
. . . But if the general topic of our discourse is 
theatres or ball games or decorations, the meaning 
. . . of 'star' will likely be very different." From 
these and similar illustrations it is evident that the 
meaning of what is asserted in any judgment is 
rendered particular as much by virtue of what it 
presupposes, that is by its universe of discourse, as 
by what it definitely asserts. We may say, conse- 
quently, that it is the intention of every judgment 
to acknowledge the truth of what it asserts in the 
sphere of what the judgment presupposes, that is, 
in some definitely implied universe of discourse. 
To apply this view to another case, we may say that 
the statement, 'Mr. Wilson was elected by the pop- 
ular vote of the people,' asserts a fact that qualifies 
in a unique way the political history of the United 
States, and not a fact that sets Mr. Wilson, by 
virtue of his election to the presidential office, apart 
from his fellow citizens. Mr. Wilson's citizenship 
is unaffected by his election, and, therefore, it can- 
not be in respect of this that our judgment is sig- 
nificant, but the election does determine in a par- 
ticular way the political history of the Republic, 
and this, therefore, must, in logical terms, be the 
universe of discourse within which our judgment 
of the election must be understood to fall. 

It follows from this view of the judgment that 
the universe of discourse implied by any judgment 



54 A TEXT-BOOK OF LOGIC 

exists always in a relatively indeterminate and 
incomplete form. This statement does not mean, 
although it is sometimes true, that particular judg- 
ments indicate only vaguely the universe within 
which their meaning is asserted. It means rather 
that, in the particular which the judgment asserts, 
the universe is found to be either not determined 
at all, or not to be determined with an explicitness 
that renders it serviceable for an immediately con- 
trolling purpose. Whatever degree of determinate- 
ness the general field or subject presupposed by any 
of our judgments may have, that field or subject 
can be used as a universe only if it is thought 
capable of receiving, through judgment, a more 
concrete and determined form. But it also follows 
from the view we are developing that judgments 
themselves are incomplete and point beyond them- 
selves. They are, as it were, fragments torn from 
their contexts; but, even so conceived, they carry 
with them, as a rule, evidence of their connection 
with the contexts from which they have been torn. 
Unless this were so, single judgments would always 
remain ambiguous. But if this were the case, if, 
that is, there existed even a considerable number 
of judgments from which we are unable to remove 
their ambiguity, because they do not point with 
sufficient definiteness to an interpreting context, the 
fact that, apart from such contexts, they remain 
ambiguous is in itself evidence that they lack some- 
thing which is characteristic of significant asser- 
tions. The meaning, therefore, of any judgment is 



THE JUDGMENT 55 

the meaning that it comes to have by virtue of its 
pointing relevantly to something which is not iden- 
tical with the relational content asserted by it. In 
so far then as a judgment has to be supplemented 
by what its context supplies, so far is it incomplete; 
and if this incompleteness is to be overcome, it must 
be by what the judgment enables us to add through 
its presuppositions. 

If, in view of this discussion, we now define the 
judgment, more fully than we have done hitherto, 
as an assertion of, or of something about, the reality 
presupposed by the judgment, we are immediately 
confronted with a question concerning the kinds of 
reality presupposed by our various judgments. In 
respect to this question, it has been maintained, for 
example by Bradley, that the real subject of which 
the thought-contents asserted by all our judgments 
are predicated is the totality of really existing things 
which we call the universe. Whatever any judg- 
ment asserts, just that, so it is maintained, is as- 
serted of reality in the sense of the system of inter- 
related existences known as the universe. Reality, 
according to this view, is always that about which 
we judge, and our particular judgments assign to 
it, as its subject, the concrete details which such 
judgments assert. On this view, no question as to 
what is the universe presupposed by any judgment 
could arise, or if it did, it would be answered before 
it was asked. 

Now, in considering this view, we do not need 
to inquire whether in the end we should be obliged 



56 A TEXT-BOOK OF LOGIC 

to take some such position as has just been stated, 
although there seem to be difficulties in the way 
of its adoption; what rather is more to our present 
purpose is to remark that such a statement does not 
represent the actual circumstances in which many 
of our concrete acts of judgment are made. For 
instance, the series of judgments in which the 
ancient mythologies state the relations of the gods 
and goddesses to one another, and to natural events 
and human history, cannot be said to be made of 
the universe of really existing objects in the sense 
that the series of judgments which constitute the 
body of one of the natural sciences can be said to 
be made of that universe. If, further, we consider 
the judgments in which we express social, ethical, 
and aesthetical facts and relations, judgments, as 
we have seen, which are not descriptive in the sense 
that scientific judgments are descriptive, but which 
refer human behaviour and natural phenomena to 
a norm or standard, it is difficult to maintain that 
these are made with immediate reference to the 
universe which sums up in itself all that may be 
called real. Whether the facts and relations that 
constitute the subject-matter of mythology, of soci- 
ology, ethics, and aesthetics can be asserted of the 
universe of which the facts and relations of the 
natural sciences are asserted, is not the question 
that confronts us; the question rather is whether, 
in the acts of judgment which give definite form 
to our knowledge of these subjects, they are so 
asserted, or whether they are asserted of other 



THE JUDGMENT 57 

universes than the one which is existentially real. 
If we admit, as we must, the latter alternative, if, 
that is, we admit the existence of a number of uni- 
verses, other than the real, within which judgments 
may fall, the question whether the real universe 
includes all these, as is sometimes maintained, is 
still left open, and we do not need to close it, for 
the reason, if for no other, that the problem involved 
belongs to metaphysics rather than to logic. Logic 
is interested in the question only for the purpose of 
emphasising the importance of ascertaining the 
universe in relation to which, as a matter of fact, 
particular judgments are asserted as the condition 
of correctly interpreting such judgments. Thus if 
we were confined to the view we are criticising, the 
assertion that 'Fishes are animals which get their 
oxygen from the water in which they live through 
gill slits/ and The Royal dragon of China has five 
claws' would have to be taken as qualifying a single 
universe ; but surely no one not blinded by a theory 
could fail to observe that in the former case we are 
asserting in the world of zoological fact, and in the 
latter in the world of Chinese heraldic design. The 
view, therefore, that seems most serviceable, and 
the one which keeps closest to the facts of our ordi- 
nary experience, is the view that emphasises the 
importance of bringing particular judgments into 
relation with their immediate contexts whatever 
these may be, and warns us against resolving the 
distinctions by which these contexts are character- 
ised into a single context about which the only 



58 A TEXT-BOOK OF LOGIC 

intelligible thing that can be said is that, in some 
sense, it is real or exists. In this connection it may- 
be remarked that for logic the important question is 
in what sense the reality or truth of an assertion 
is to be understood. 

Truth, Probability and Error. Truth, probability 
and error, as employed in logic, are terms which 
describe characteristics that belong to assertions, 
they are never employed, as they sometimes are in 
popular speech, to designate qualities of the objects 
about which the assertions are made. From the 
standpoint of logic, objects exist, and they are only 
the assertions which are made about particular 
existing things that are said to be true, probable, 
or erroneous. Truth, probability, and error, then, 
can never be predicated of things, but only of our 
judgments of, or about, things. 

Now, since all judgments claim to be true, we 
have to inquire what we mean by truth, and how 
there can be such things as probability and error. 
With regard to the meaning of truth, it is pretty 
generally agreed that the notion is so nearly ulti- 
mate that we find it difficult, if not impossible, to 
offer a definition which does not involve the notion 
itself as one of the terms. But if truth cannot be 
defined, we can describe, in a more or less satis- 
factory manner, what we mean when we use the 
word. We may say, then, that an assertion is 
true when it assigns a character to the elements 
and relations of a subject-matter which are found 
to be verified when this subject-matter is investi- 



THE JUDGMENT 59 

gated by appropriate methods. Thus the judgment, 
The fire is hot,' is true, if, when I put myself into 
sufficiently close proximity to the fire referred to, 
I experience the sensation called heat. Truth, then, 
is not a quality of judgments merely as such; it is 
a quality that belongs to judgments ad hoc, that is, 
as assertions of definitely specified contents. When, 
in other words, the ideas conveyed by a judgment 
are such that, in the universe presupposed by the 
judgment, there are facts which exist in the manner 
it asserts, the judgment is said to be true. Truth, 
that is to say, is always a claim that is set up on 
behalf of a judgment's object, in behalf, that is, of 
what Meinong called the judgment's 'objective.' 

In view of this general statement, it may be 
asked whether any judgment is true, or whether 
judgments are at best only probable. The answer 
to this question obviously depends upon whether we 
ever need to go beyond a judgment's assertion to 
ascertain whether the facts and relations asserted 
by it are as they are asserted. When, for example, 
we assert that The sun is the source of the world's 
heat,' it is obvious that the verification of the asser- 
tion must be sought in astronomical physics, that, 
in other words, the judgment is true conditionally 
upon our being able to verify, in the appropriate 
universe, the facts and relations asserted in the 
judgment. But not all our judgments are, in this 
sense, assertions about a given subject; judgments 
are also assertions of a given subject. If, for ex- 
ample, we say, The subject about which we are 



60 A TEXT-BOOK OF LOGIC 

thinking is the sun as the source of the world's 
heat,' it is obvious that, whatever physics may have 
to say about this particular subject, it can have 
nothing to say that throws doubt upon the fact that, 
at the time the assertion is made, we are actually 
thinking about this particular subject. We select 
an illustrative example from the world of physical 
objects because arguments for the absolute contin- 
gency of truth have sometimes been framed on the 
supposition that contingency can be removed only 
when all the factors of the judgment are merely 
states of one's own mind. It is often said, for instance, 
that the certainty that belongs to mathematics 
is rendered possible by the fact that the fundamental 
notions of mathematics are concepts and not really 
existing things. Whether this view of mathematics 
is correct or not, it is certain that the judgments 
which assert these fundamental notions are no more 
indubitable than are those judgments which assert 
some object in the physical world as the object of 
thought's activity. It would seem to follow, there- 
fore, that all judgments which are assertions of 
particular objects as the objects of thought are true 
in the sense that it is not possible for those who 
entertain them to be in any doubt that those are 
the objects with which thought is engaged. 

Judgments which make assertions about, and 
are not merely assertions of, their subject-matter 
are in a different position from those just considered. 
The chief difference is that in their case we have 
to go outside the judgment's assertion for the veri- 



THE JUDGMENT 61 

fication of the truth of what such judgments assert. 
The grounds, that is to say, on which the truth of 
these judgments rest are to be found in the universe 
to which what the judgment asserts is known to 
belong. The fact to which attention is in this way 
being directed is that the assertions we make about 
the objects of our experience do not derive their 
truth from the fact that they are asserted, but from 
the fact that there can be shown to exist in a given 
universe facts and relations of the kind that our 
judgments assert. This interpretation of the truth 
of our judgments should not come as a surprise to 
those who have followed the discussions of this and 
the preceding chapters, for the demand for a test 
of truth is after all merely a challenge to refer one's 
judgments back to the conditions which, in the first 
place, made them possible. In this way we are 
enabled to show that, when all the motives that, 
in the first place, conditioned the judgment are 
operative, the assertion contained in it is just the 
assertion that that situation compels us to make. 
Thus when the chemist's assertion that the liquid 
contained in a particular bottle is sulphuric acid is 
called in question, he does not attempt to prove the 
truth of his judgment by an emphatic restatement 
of it, nor by any form or number of reiterations; 
what he does, if he wishes to remove the doubt that 
the question has raised, is to apply the tests for 
this substance which, in the first place, convinced 
him that it was sulphuric acid and not something 
else. We may conclude, therefore, with reference 



62 A TEXT-BOOK OF LOGIC 

to the class of judgments under consideration that 
their truth is conditional upon our ability to apply 
tests of a kind suitable to the character of the 
subject-matter about which the assertions are made, 
for it is only when tested that we are able to com- 
pare what is asserted with what happens in situ- 
ations similar to those in which the judgments in 
question originated. In the absence of such tests, 
judgments of this class can only be said to have more 
or less probability. 

There are situations, however, in which we are 
either unable or unwilling to verify our judgments, 
and are thus precluded from determining the par- 
ticular degree of credibility that properly belongs 
to them. In these cases, the claim to truth which 
all judgments maintain on their own behalf can be 
acquiesced in as little as it can be dissented from. 
There belongs, consequently, to the judgments in 
question the probability that attaches to any unver- 
ified assertion from whatever cause it may arise. 

It is because so large a number of our social 
judgments are incapable of the strict proof that 
can be insisted upon when the subject of the judg- 
ment is some part of the material universe that, 
as a class, they have generally been regarded as 
possessing a lower degree of certainty than that 
which seems to belong to some of the established 
conclusions of the natural sciences. We cannot 
revive in the form of actually existing situations, 
for example, the circumstances which determined 
our actions of a week ago, and we cannot, therefore, 



THE JUDGMENT 63 

verify the judgments of which these actions are 
the practical expression. That at the time indicated 
and in relation to the situation then existing we did 
judge so and so, is as certain as any judgment can 
be; but that the judgment at which we then arrived 
was true is, in the nature of the case, beyond the 
possibility of strict proof. It would certainly be a 
very gratuitous form of scepticism to repose no 
confidence whatever in any social judgment, because 
all such judgments labour under this disadvantage ; 
and to suggest its possibility is sufficient to expose 
the absurdity of such a course. For it may be 
affirmed that the disadvantage in question is not 
confined to the social judgments we are now con- 
sidering. It may be urged that some of the judg- 
ments that are made about the material universe 
are incapable of the experimental proof to which 
our exposition has pointed as the test of truth. Our 
belief that the sum total of physical things is a 
universe, is, that is, a sphere of material existences 
whose changes are all subject to law, is not beyond 
question; and when the belief is challenged, as it 
has been recently, we cannot put the material uni- 
verse itself in evidence on either side of the ques- 
tion. Such a belief, and the judgment in which the 
belief is asserted, can have no other kind of cer- 
tainty than that which belongs to the social judg- 
ments of which we have in particular been speaking. 
Current belief undoubtedly regards the moon as a 
sphere, but, on account of the particular configura- 
tion of the solar system, it can never be a practically 



64 A TEXT-BOOK OF LOGIC 

demonstrated fact that the side which is always 
turned away from our earth is not flat. Ether, 
ions, centres of force, and atoms themselves are all 
subject to the same kind of doubt, whenever any 
one, for what seems to him sufficient reasons, is 
inclined to call them in question. In view of these 
instances, it is only fair to conclude that judgments 
about any sort of material must be regarded merely 
as probable whenever we are unable to show that 
facts and relations of the kind asserted do exist in 
the universe that is presupposed by these judgments. 
Again, judgments must be classed as probable 
whenever we are unwilling, for a reason that seems 
sufficient to us, to apply the test of truth. When, 
for example, one refuses a cup of coffee of one's 
hostess with, 'No, thank you; coffee always means 
a sleepless night,' the judgment by which we excuse 
or explain our refusal has no doubt a certain prob- 
ability derived from past experience, but it is one 
that, for prudential reasons, we are unwilling to 
verify in the particular circumstances which are 
the occasion of its assertion. Sleepless nights, we 
may admit, have followed the drinking of coffee in 
the past, and it is anticipated that a similar result 
will follow on the present occasion. In a case like 
this, which is typical of many others that involve 
future consequences rather than past acts, we should 
be going beyond the bounds of necessity if we ac- 
ceded without reservation the certainty that the 
judgment claims on its own behalf. We feel, per- 
haps, that the judgment in question has a high 



THE JUDGMENT 65 

degree of probability, but whether it deserves the 
confidence, say, that is commonly reposed in the 
prediction of a solar eclipse, is a matter upon which 
it is not necessary to dogmatise. It is more to the 
point to observe that the class of judgments that 
we are discussing is conditional, and, consequently, 
that it is only if we suppose the present situation 
is in all essential respects similar to those in which 
the consequence has followed in the past, that we 
have sufficient reason for believing that a like con- 
sequence will follow on the present occasion. But 
it is exactly this supposition of which the judgment 
itself is unable to give assurance, and which there- 
fore renders the judgment less than certain until 
it is submitted to the process of proof. 

We may now pass to the meaning of error. 
And, in the first place, error must be distinguished 
from mere irrelevance. Irrelevance may exist in 
either of two forms. It may exist, first, as an in- 
compatibility in the content of what a judgment 
asserts. If, for example, Shylock's bond had been 
drawn for a pound of justice, and not for a pound 
of flesh, there would have been an irrelevance of the 
kind in question, because the avoirdupois scale can- 
not in any sense be made the measure of justice. 
The universe suggested by the assertion, 'I will 
have a pound of justice/ is one in which the content, 
on account of its internal contradiction, cannot pos- 
sibly get realised. Irrelevance in this form, then, 
arises whenever we predicate of a subject qualities 



66 A TEXT-BOOK OF LOGIC 

and relations which cannot be realised in the uni- 
verse to which the subject is thought to belong. 
Instances of this occur whenever we attribute to 
purely natural events moral or aesthetic significance, 
or when we explain any of our ideals in terms of 
mechanical causation. Secondly, irrelevance may 
exist as an incompatibility between what is asserted 
and the purpose by which the assertion is controlled. 
What in these instances is asserted may be true, as, 
for example, 'Mont Blanc is snow-capped all the 
year round,' but no one would think of making or 
entertaining the assertion in a discussion on the 
value of Rotterdam as a Dutch port of entry to the 
German Rhine. Failure to understand the limita- 
tions that a guiding purpose or interest imposes on 
what may and what may not be significantly asserted 
about a given subject-matter is one of the most 
fruitful sources of confusion in discussions of all 
sorts, and it is to this form of irrelevancy that we 
look for the origin of those half-truths which do 
more mischief in the world than frank and un- 
blushing error. The comment is worth while in 
this connection because it is to the avoidance of 
such irrelevance that the student may look as one 
of the means of hastening his academic and prac- 
tical efficiency. In either of the two forms which 
we have now distinguished, then, irrelevance is not 
to be identified with error. 

Error, in contrast with the second of the two 
forms of irrelevance just distinguished, is an asser- 
tion which is relevant to a purpose, and, in contrast 



THE JUDGMENT 67 

to the first, is an assertion whose contents are com- 
patible. Unless it possessed both these marks of a 
true judgment, error could not possibly exist. To 
emphasise the former contrast, we may say that 
error is ascribed to any judgment which, if true, 
would satisfy the purpose for which the judgment 
is made. There follows from this statement a con- 
sideration which is important for all our judgments, 
namely, that the range of assertion about any 
subject-matter is determined at the outset by the 
character of the purpose which stimulates and 
directs the judging process. In other words, to 
expect our judgments to be true is a perfectly rea- 
sonable expectation, but to expect that they will 
assert the whole truth is to convict our expectation 
of being either unmeaning or false. The latter 
expectation is indefensible for the same reason that 
the former is maintained, namely, that we do not 
as a rule, nor can any reason be advanced why we 
should, encumber our judgments by asserting non- 
significant features of the subject-matter to which 
these judgments refer. And if it is asked, 'What is 
and what is not significant?' we can only reply that 
that all depends upon what the judgments is wanted 
for. The truth of this statement can be readily 
seen in what occurs when all interest in a question 
vanishes. In such a situation nothing whatever 
can get asserted. But when an assertion is made, 
it must be made, not merely of something, but for 
some purpose, and it is the character of the purpose 
that determines what feature of that 'something' 



68 A TEXT-BOOK OF LOGIC 

is selected for assertion. There is, for example, no 
doubt that the grass is green and, let us say, that 
it is long, but it is only the latter assertion that is 
pertinent when one has to decide what instructions 
to give the gardener about the day's work. What 
one thinks about any object, say a house, depends 
upon whether we are considering it architecturally, 
domestically, or as an investment. These interests, 
no doubt, overlap, but they are sufficiently distinct 
to make quite irrelevant certain assertions that 
might be made from one of these points of view 
when, as a matter of fact, we are considering it 
from one of the other points of view. But we do 
not call judgments false which bear no relation to 
the interest by which the judging process is initiated. 
Error as well as truth exist only in those judgments 
which claim to fulfill the purpose of the individual 
by whom they are asserted. 

The second contrast stated above calls attention 
to the fact that the contents of erroneous judgments 
are, as we said, compatible. That is to say the 
judgment must assign its content to a sphere in 
which it is possible for that content to be realised. 
The absence of incongruity between the elements 
of what is asserted is a characteristic of error as it 
is of truth. When, for example, we judge that an 
object is elliptical when in reality it is round, we 
are in error, but the error does not consist in 
assigning it a shape, but in attributing to it the 
wrong shape. The wrong shape, however, is an 
antecedently possible shape, and it is upon this ante- 



THE JUDGMENT 69 

cedent possibility that the erroneous character of 
the judgment rests. If instead of asserting that the 
object was elliptical we had asserted that it was 
blue, we should not regard that as an error; we 
should regard it either as a misunderstanding of 
the motive of the judgment or as nonsense. 

We are now in a position to state what error is. 
The problem of error is greatly simplified when it is 
observed that no judgment which fails to assert 
those features of its subject-matter which are perti- 
nent to the purpose in hand could by any possibility 
be regarded as true or erroneous. They are, as we 
saw, merely irrelevant. It is only when judgments 
offer themselves as the means of satisfying a pur- 
pose that they are ever entertained. There is, there- 
fore, from the standpoint of the interest involved, 
little chance for error. All that we can say about 
a judgment, from this point of view, is that it does 
more or less completely fulfil a present purpose. It 
is, therefore, to the character of what is asserted 
that we must look finally for the detection of error. 
And here, as in the coresponding case of truth, we 
are confronted with a simple question of fact. Is 
it a fact, we must enquire, that there exist in the 
universe presupposed by the judgment qualities and 
relations of the kind asserted in the judgment? If 
there are, we call the judgment true; if there are 
not, we call the judgment erroneous. Error, then, 
may be defined as some discrepancy between asser- 
tion and fact. 



70 A TEXT-BOOK OF LOGIC 

We have been speaking in this section of error 
as a failure of the judgment to assert the significant 
qualities and relations of the object upon which 
thought is directed. The term is also used to denote 
those mistakes of judgment which depend, for ex- 
ample, upon inference. In this sense it is preferable 
to speak of fallacies. A discussion of this subject 
will be found in the concluding chapters of this 
book. 

REFERENCES 

H. A. Aikins, The Principles of Logic, Ch. I., II. 
B. Bosanquet, The Essentials of Logic, Lect. II., III. 
J. E. Creighton, An Introductory Logic, 3d Edition, Ch. XXI. 
J. G. Hibben, Logic, Deductive and Inductive, Part I., Ch. III. 
W. S. Jevons, Lessons in Logic, Lessons VI., VII. 
S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
tion, Ch. I. 

ADVANCED 

J. M. Baldwin, Thought and Things, Vol. I., Ch. XL, §§4-8; 

Vol. II., Ch. II., VI., §§ 1-4. 
B. Bosanquet, Logic, Book I., Ch. I. 
F. H. Bradley, The Principles of Logic, Book I., Ch. I. 
W. R. B. Gibson, The Problem of Logic, Ch. IX. 
H. W. B. Joseph, An Introductory Logic, Ch. VII. 
H. Lotze, Logic, Book L, Ch. II. 
J. S. Mill, A System of Logic, Book I., Ch. II. 
F. C. S. Schiller, Formal Logic, Ch. VIII. 
J. Welton, A Manual of Logic, Vol. I., Ch. I., II (ii). 

QUESTIONS 

1. What general meaning may be given to the term object? 

2. In what several ways may we be acquainted with 
objects? 






THE JUDGMENT 71 

3. Is the character of an object affected by the way in 
which it is apprehended? 

4. What do you understand by objects being implicated 
in all mental processes? 

5. Distinguish three senses in which the term 'thought' 
has been used, and state how they are related to each 
other. 

6. To which of the meanings already distinguished is 
thought, from the logical point of view, most closely 
related ? 

7. What particular aspect of thought does logic emphasise 
in its use of the term judgment? 

8. What is meant by saying that the subject-matter of 
judgment is the content of a thought process? Illus- 
trate. 

9. Explain : 'Judgment is an assertion of the qualities and 
relations of the objects of thought.' 

10. Is language necessary to give thought the character of 
assertion? Explain. 

11. State clearly what you understand by assertion. Illus- 
trate. 

12. Show in what ways judgments are implied, but not ex- 
pressed, in interrogatives, imperatives, optatives, and 
exclamations. 

13. Describe what is meant by groundless statements, and 
in what respect do they differ from judgments? 

14. Define and illustrate the practical and theoretical as- 
pects of thought processes. 

15. 'Judgments may be defined as relevant assertions.' 
How does this view of the judgment agree with and 
differ from that stated in Question 9? 

16. In what two respects may all judgments be said to be 
relevant? 

17. Explain what is meant by saying that judgment is 
based in and grows out of our practical needs. Illus- 
trate. 



72 A TEXT-BOOK OF LOGIC 

18. Define what you understand by 'practical/ and show 
how unsatisfied needs of the sort here in question con- 
dition the formation of judgments. 

19. How is your answer to the preceding question affected 
by the fact that judgments are assertions about a sub- 
ject-matter of some sort? 

20. To what two kinds of error is one exposed in trying 
to show the relation of thought to its object? 

21. Explain and illustrate what is meant by saying that 
the interest that conditions a judgment may be extrinsic. 

22. What do you understand by a value judgment? 

23. Describe the nature of scientific interest, and explain 
why it may be called, in contrast to other kinds of 
interest, intrinsic. 

24. Is judgment to be distinguished from awareness of an 
object? Explain. 

25. What difference, if any, do you recognise between the 
subject and the object of judgment, and illustrate by 
referring to Bradley's distinction between the 'that' and 
the 'what.' 

26. Explain what Meinong means by the 'object' and the 
'objective' of logical judgments. 

27. How may Meinong's distinction be correlated with the 
view taken in the text? 

28. 'Judgment may be defined as an assertion of, or of 
something about, the objects of our experience.' Explain 
this statement, and correlate it with the definitions of 
judgment in Questions 9 and 15. 

29. ~Why is the definition of judgment given in the preceding 

question not completely satisfactory? 

30. What do you understand by a universe of discourse? 
Illustrate. 

31. Why must any universe of discourse have a more or 
less indeterminate character? 

32. Why must single judgments be regarded as incomplete, 
and, therefore, as being to some extent ambiguous? 

33. How may this ambiguity be overcome? 



THE JUDGMENT 73 

34. 'Judgment may be defined as an assertion of, or of 
something- about, the reality presupposed by the judg- 
ment.' Explain and compare with other definitions 
given in Questions 9, 15, 28. 

35. What, according to Bradley, is the universe presup- 
posed by all our judgments? 

36. What objections can you urge against Bradley's view? 

37. Is there a plurality of universes? Justify your answer 
and illustrate. 

38. Of what are truth, probability and error predicated in 
logic? 

39. In what respect does the logical differ from the popular 
use of these terms? Illustrate. 

40. What i& the logical meaning of truth? Illustrate. 

41. Of what class of logical judgments can you say that 
they are certainly true? Illustrate. 

42. Can the truth of any of our judgments about a given 
subject-matter be maintained? State reasons for your 
answer, and illustrate. 

43. What two conditions compel us to regard certain of our 
judgments as probable, not true? 

44. Why do we generally regard judgments about social 
material merely as probable? 

45. Do similar reasons apply to any of our judgments about 
the material world? Explain and illustrate. 

46. How does unwillingness to verify an assertion affect its 
claim to be true? 

47. In what two forms may irrelevance exist? Explain and 
illustrate each. 

48. How do you distinguish irrelevance from error? 

49. Why do we not call those judgments which fail to fulfil 
a purpose erroneous? Illustrate. 

50. What is meant by saying that in order to be erroneous 
judgments must assert contents that are compatible? 
Illustrate. 



.74 A TEXT-BOOK OF LOGIC 

51. Wherein consists the nature of error? 

52. Can you frame a definition of error? 

53. In what respect does error differ from fallacy? 

EXERCISES 

1. In what sense is the word, thinking, used in the follow- 
ing statements : 

(1) All human beings are thinking beings. 

(2) There is no truth or error but thinking makes it so. 

2. State at least two judgments about each of the follow- 
ing subjects: 

(1) Mathematics as a required subject for college grad- 
uation. 

(2) Inter-collegiate football as a desirable form of stu- 
dent activity. 

3. What are the grammatical forms of the following, and 
show in what sense they may be said to involve judg- 
ments : 

(1) O wad some power the giftie gie us 
To see ourselves as others see us. 

(2) How oft the sight of means to do ill deeds 
Makes deeds ill done. 

(3) Can one desire too much of a good thing? 

(4) Are things what they seem? 
Or is visions about? 

(5) Give me that man 
That is not passion's slave, and I will wear him 
in my heart's core, ay, in my heart of hearts, 
As I do thee. 

4. Give six illustrations of what are called groundless 
statements. 

5. State six judgments on subjects of your own choosing 
that show the influence of purpose on the judging 
activity. 

6. Give six illustrations of the way that judgments are 
controlled by the nature of the subject-matter about 
which one thinks. 



THE JUDGMENT 75 

7. Take three instances of judgment from your answer to 
Question 5, and the same number from your answer to 
Question 6, and show in each case the relation of interest 
to subject-matter. 

8. Take the remaining instances from your answers to 
Questions 5 and 6, and state what is the subject and 
the object in each case. 

9. What can you say about 'water' in each of the following 
universes of discourse: domestic life; chemistry; phys- 
ics; art; physiology. 

10. Examine the following judgments, and state whether, 
and under what conditions, you regard them as true, 
irrelevant, probable, or erroneous : 

(1) Everything comes if a man will only wait. 

(2) For a man's house is his castle. 

(3) The many still must labour for the one. 

(4) Thought is free. 

(5) Virtue is its own reward. 



CHAPTER III 
THE PROPOSITION 

Judgment and the Proposition. In text-books of 
logic, it is usual to discuss the judgment and the 
proposition in the same chapter, and to emphasise 
the points of similarity between them. In the pres- 
ent chapter, we are to consider the proposition by 
itself, because in this way we shall be able not only 
to distinguish between it and the judgment, but to 
group together certain problems that arise out of 
the nature of the proposition which are more or less 
distinct from those of the judgment which were dis- 
cussed in the previous chapter. 

In its most general meaning, a proposition may 
be defined as the verbal expression of a judgment. 
As we proceed, this statement will be made more 
explicit; but it will suffice for our present purpose 
if it enables us to understand the importance of put- 
ting into verbal form the truths that are asserted 
in our judgments. The necessity of finding a suit- 
able medium for expressing our judgments is forced 
upon us when it is realised that explicit statements 
of our meanings are, sometimes, if not frequently, 
important factors in our search for truth. We often 
find, for example, that ideas with which we had sup- 
posed ourselves perfectly familiar suddenly take on 
a penumbral haze when we are required to use these 
ideas in working out new problems, — for instance, 

(76) 



THE PROPOSITION 77 

in solving an 'original' in geometry or in finding an 
'unknown' in chemistry ; or when we try to commu- 
nicate these ideas to other people, — for instance, 
in a class recitation. In both these cases, we have 
before us the task of setting the ideas in question 
in a different context, and it is the new context* into 
which they are to be fitted that reveals to us .defects 
in the ideas themselves of which we were hitherto 
unaware. In order to succeed in the problem that 
is thus presented, it often becomes necessary to give 
verbal expression to our ideas, and our search for 
the suitable form is not infrequently found to re- 
act upon the ideas themselves to make them more 
exact. It may also be noticed that when we have 
once expressed our ideas in accurate verbal forms, 
we are able to analyse these ideas, and thus to ad- 
just them to other ideas with which they have 
various relations. For it must be admitted that our 
interest in ideas is not merely to know that they are 
true, but, concurrently with this, to use them in en- 
larging the boundaries and directions of our knowl- 
edge. And it contributes to both these objects to 
secure for our ideas an adequate verbal expression. 
The statement of our judgments in the form of prop- 
ositions both clarifies the meaning and renders the 
application of our ideas possible. 

We may bring out the difference between the 
judgment and the proposition if we refer to the way 
that each originates in our ordinary experience. In 
the foregoing chapter, we have had occasion to indi- 
cate in a general way the conditions under which our 



78 A TEXT-BOOK OF LOGIC 

judgments arise. Judgments were there described 
as completed solutions of problems set by the situ- 
ations in which one finds himself from time to time. 
That is to say, judgments arise out of whatever is 
problematical, undetermined, baffling, whether this 
falls in the sphere of perception, or in the sphere 
of the social, scientific, ethical, sesthetical, or relig- 
ious life. Whatever sets a barrier to the satisfac- 
tion of wishes, whatever hinders, arrests, or makes 
impossible the carrying out of cherished plans, chal- 
lenges and stimulates the life of thought, and forces 
us into a judgment. Judgments arise out of our 
needs for knowledge, and this need is stimulated 
when the situation which instigates the need is of 
such a character that our way to the successful con- 
duct of the theoretical or practical life is blocked. 
When we have unravelled the tangle, and see the 
total situation in its bearing upon our arrested pur- 
suits so that we either modify or change our aims, or 
they are given an open field, we may be said to have 
judged. It is another story when we ask what are 
the conditions that determine the rise of proposi- 
tions. In the proposition we are not seeking to 
extricate ourselves from an embarrassment, because 
no embarrassment is present, and we are not seeking 
knowledge, because that already exists. A proposi- 
tion, as we have already said, is the verbal statement 
of what we already know ; it is a statement in which 
something is either affirmed or denied of something 
else. It is, consequently, not an instrument of the 
search for knowledge, but of its communication. 



THE PROPOSITION 79 

When we put our judgments into propositional form, 
we are making* them socially available, and present- 
ing them for acceptance or rejection. 

The Import of Propositions. A proposition may 
be interpreted from either or both of two points of 
view : from the point of view of the person speaking, 
and from the point of view of the person spoken to. 
In each of these cases, the proposition has a different 
import or meaning. In the former, where the person 
speaking is expressing a judgment concerning a sub- 
ject about which he has reached a conclusion, the 
proposition means what the judgment which it ex- 
presses means, and must be interpreted as a judg- 
ment. That is to say, the truth of the proposition 
is also the truth of its corresponding judgment, and 
vice versa. The meaning of the proposition, inter- 
preted from the point of view of the speaker, i? 
designated in logic as the truth-import of the propo- 
sition. In the other case, when we consider the 
proposition from the standpoint of the hearer of it, 
the proposition and the judgment which it expresses 
are not the same, and the truth they express may not 
be identical. The reason why the proposition may 
mean one thing to the hearer and another to the 
speaker must be looked for in the differences of the 
relations that the hearer and speaker have to the 
knowledge that the proposition embodies. Or, to 
put the matter more definitely, the speaker's rela- 
tions are with the knowledge which the proposition 
expresses, while the hearer's are with the terms of 
the proposition itself. When we interpret a propo- 



80 A TEXT-BOOK OF LOGIC 

sition from the standpoint of the person spoken to, 
we have what is called in logic the statement-import 
of the proposition. The statement-import is, conse- 
quently, a structural interpretation of the proposi- 
tion ; it is the meaning that a proposition has when 
it is considered from the standpoint of its factors 
or terms. 

We may look at this distinction between the 
statement-import and the truth-import of proposi- 
tions a little more in detail. It is obvious that the 
question before the speaker is one of selecting the 
words that will adequately convey his meaning. 
When one wishes to make a judgment socially avail- 
able, one has to express the judgment in words, or in 
some other recognised means of communication. 
When, on the other hand, we listen to what is said, 
or read what is written, the question before us is to 
ascertain the meaning that the words were originally 
intended to convey. This is not always as simple as 
it may sometimes seem. Because, for example, the 
words in which we are addressed are familiar, it does 
not follow that the idea that the words express is at 
all understood. The common misunderstandings of 
ordinary life, and the more serious difficulties that 
we meet with in the course of our studies, are due 
very often to our failure to interpret aright the 
meaning, not to our inability to understand the 
words, of the propositions that are laid before us. 
In such a case, the proposition means for us some- 
thing that it does not mean for the speaker; it has 



THE PROPOSITION 81 

for us, that is to say, a statement-import but no 
truth-import. 

It will help our understanding of this statement 
if we throw the essential factors of our problem into 
the form of a diagram : 

Speaker Hearer 



r \ r -\ 

Idea *■ Proposition •- Idea 

v _ j \ J 

Y Y 

Truth-import Statement-import 

If, reading the above diagram, our interpretation of 
the proposition is made from the standpoint of the 
speaker, we start with the idea or judgment that has 
to be expressed in the proposition; the proposition 
is then the verbal expression of the judgment or 
idea from which we set out. For the speaker, the 
proposition does express his judgment, and so inter- 
preted it embodies the truth of his judgment. If, 
on the other hand, our interpretation is made from 
the standpoint of the hearer, we start with the prop- 
osition, the verbal expression of the speaker's judg- 
ment, and the words of the proposition have to be 
interpreted so as to render an idea or judgment pos- 
sible. But what is the guarantee in such a case that 
the meaning derived from the proposition will be 
the meaning expressed by it? The idea in the 
hearer's mind may be different from the idea in the 
speaker's mind. It is this idea, the idea or meaning 
that the hearer of a statement gets from what is said 



82 A TEXT-BOOK OF LOGIC 

to him, that we designate the statement-import of 
the proposition. The truth-import and the state- 
ment-import of a proposition, therefore, may not be 
the same. 

But, it may be asked, does not our interpretation 
of a proposition, even when it is taken from the 
standpoint of the hearer, aim at an identity of mean- 
ing between its truth-import and the statement- 
import? This is doubtless true. But we should 
miss a great deal in our understanding of the life of 
thought if we did not see the possibility of the same 
statement meaning different things for speaker and 
hearer. It is this fact that we have been emphasis- 
ing. And it is as desirable to ascertain how this 
difference may arise as to see how it may be over- 
come. For if we understand the origin of such dif- 
ferences, we shall know how to avoid or overcome 
them. In either case, we are concerned with the 
context of the idea or judgment that we are trying 
to understand ; and it is obvious that when the con- 
text is different for speaker and hearer, the idea 
the proposition conveys must, in some measure, be 
different for both. For, as we have seen, the con- 
texts in which our ideas occur give part of the mean- 
ing that ideas may have. If, therefore, you change 
the contexts you change also in part the ideas them- 
selves. Thus, whenever we fail to get the meaning 
of what is said to us by reason of our failure to 
understand the universe of discourse within which 
the thought of the speaker is moving, we do not 
naturally ask for a repetition of the sentence or 



THE PROPOSITION 83 

proposition, but require, for its comprehension, a 
larger section of the context, and, in some cases, the 
revival of the whole universe within which the truth 
of the judgment is, by the speaker, presumed to 
exist. In other words, it is the fragmentariness of 
all our judgments, to which reference has been made, 
that is the ground of the difference between the 
truth-import and the statement-import of proposi- 
tions ; a fragmentariness that can be overcome only 
if it is supplemented by a larger portion of the inter- 
preting context than is frequently implied by the 
single proposition. 

We may further elucidate the important distinc- 
tion just made between the truth-import and the 
statement-import of propositions if we consider it 
as a special instance of the difference, first drawn 
by the English historian, Grote, and made current 
by the American psychologist, James, between 
"knowledge of acquaintance" and "knowledge 
about." An illustration sometimes used to indicate 
the contrast between these two kinds of knowledge 
is the difference between the normal child's expe- 
rience of light, and the experience of light that a 
child, blind from birth, has through the reports of 
seeing adults. The knowledge of the two children, 
without doubt, is at different removes from the real 
character of light. That is to say, the contrast be- 
tween "knowledge of acquaintance" and "knowledge 
about" calls attention to the fact that the knowledge 
that any one has is sometimes immediate and direct, 
and sometimes mediate and indirect. Now, the dis- 



84 A TEXT-BOOK OF LOGIC 

tinction between the truth-import and the statement- 
import of propositions seems to be contingent upon 
whether propositions express either the one or the 
other of the above-mentioned kinds of knowledge. 
We are all aware that much that we ordinarily call 
knowledge is based upon nothing more certain than 
our ability to understand the words in which this 
knowledge has been communicated, while a much 
smaller fraction of our knowledge rests on direct 
acquaintance with the facts, and a study of the rea- 
sons by which such knowledge is supported. In the 
one case, propositions embody judgments, and are 
to be interpreted as judgments; in the other case, 
propositions are statements to be understood, 
whether they introduce us or not to the facts out of 
which the judgments which they express have come. 
To understand what is told us is a first step in knowl- 
edge ; but it is only a first step, and should lead us 
beyond itself to a more intimate and personal ac- 
quaintance with the truths and facts that are the 
material of advancing knowledge. In other words, 
we must proceed from the statement-import to the 
truth-import of the propositions which convey to us 
so large a proportion of the material upon which the 
educative processes as a whole depend. 

Formal Analysis of the Proposition. The propo- 
sition was defined above as the verbal expression of 
a judgment; it is the logical instrument by which 
what is true for judgment gets a simple and un- 
equivocal expression. But not every verbal expres- 
sion of a judgment is a proposition ; it may be, for 



THE PROPOSITION 85 

example, a sentence. A sentence may be a proposi- 
tion, as, for example, 'The book is on the table;' but 
this is not necessarily the case, as, for example, 'A 
friend of mine has gone abroad.' From the formal 
side, the essential difference between the sentence 
and the proposition lies in the number of the factors 
present in each. A sentence always requires the 
presence of a subject and a predicate; the proposi- 
tion cannot exist without a subject and predicate, 
which are called terms, and also a copula. If we 
compare the sentence and the proposition in these 
respects, we shall see that the predicate of the sen- 
tence is, by logic, broken up into two parts, the 
copula and the predicate of the proposition, and that 
the subject remains the same. The following dia- 
gram represents these relations to the eye : 

Sentence: Subject Predicate 



Proposition: Subject Copula Predicate 

The doctrine of formal logic depends upon the struc- 
tural difference between the proposition and the sen- 
tence as thus outlined. In the following sections, 
therefore, we shall dwell on the meaning that logic 
assigns to the several parts of the proposition. 

Terms. The subjects and predicates of proposi- 
tions are called terms. Now, since the proposition 
is a statement in which, as we have seen, something 
is predicated — affirmed or denied — of something 
else, we may define the predicate term as that which 
is predicated, and the subject term as that of which 



86 A TEXT-BOOK OF LOGIC 

the predication is made. If, as is usual, we use the 
symbol S for the subject term, and the symbol P 
for the predicate term, the structural proposition 
may be written S — P. In such a proposition, P is 
said to be predicated of S. We may observe that 
the subject term of a proposition is always written 
first, and the predicate term last. The reason for 
this seems to be that since the proposition is deter- 
mined by the interests of communication, it is im- 
portant, at first, to call attention to that about which 
we wish to speak. If the student remembers this 
he will avoid the difficulty that is sometimes expe- 
rienced in distinguishing between S and P. For 
example, if we wished to express in propositional 
form the statement, 'Uneasy lies the head that wears 
a crown,' it would not be accurate to say that 'Un- 
easy' is the subject. The rule that may be followed, 
whenever we are in doubt as to what our terms are, 
is to ask: What am I speaking about? The answer 
to this question will give us the subject term. The 
predicate term may be found by asking, What am 
I saying of this? If we apply these tests to the 
example just cited, we shall find that we are speak- 
ing about 'The head that wears a crown,' and this, 
consequently, is the subject term of the proposition; 
and that what we are saying of this is that it is 
'uneasy,' and this, consequently, is the predicate of 
the same proposition. 

It should be remarked that we are frequently 
at a loss to know which is the subject, and which 
the predicate, term of given statements. The reason 



THE PROPOSITION 87 

for this seems to be that in order to know what any 
statement means we require sometimes to have be- 
fore us a larger section of the whole context of 
thought than the particular statement itself pro- 
vides. This takes us back to what we said above 
about 'the universe of discourse,' and the function 
it serves in giving to our particular judgments the 
meaning they are intended to have. Propositions 
express judgments which are torn loose from their 
contexts, and they sometimes do, and sometimes do 
not, retain sufficient of the original context to make 
our interpretation of them certain. The example 
that was quoted above illustrates the former case; 
we were doubtless talking about 'crowned heads.' 
A more difficult case, taken from Jevons, is the fol- 
lowing: 'Life is held dear by every man.' In this 
statement, are we talking about 'life,' or about 
'things that are held dear,' or about 'every man'? 
Grammatically, 'life' is the object of the verb 'holds 
dear,' and cannot, therefore, be the subject. The 
meaning of the statement, consequently, is : 'Every 
man holds life dear.' We are speaking in the uni- 
verse of values ; and, in the statement, we are nam- 
ing one of the objects of value. If, however, to take 
an illustration from Sidgwick, we say that 'Newman 
wrote the Grammar of Assent,' we have no means 
of determining whether 'Newman' or 'The Gram- 
mar of Assent' is the subject, because, as Sidgwick 
says, "the statement is regarded in isolation from 
all context. Regarded in this abstract way, it may 
equally well be called a statement about Newman, 



88 A TEXT-BOOK OF LOGIC 

or about the book, or again about both the man and 
the book. ,, It would seem, then, that back of all 
particular statements there lies a universe of fact 
or idea which flows over into these statements to 
give them the determinate meaning they may prop- 
erly have. 

Names and Words. Another question, closely 
connected with the foregoing, arises when we ask 
whether terms can exist outside the propositions in 
which they are found. We may ask, for example, 
whether The head that wears a crown/ which, as we 
saw, was the subject term of the proposition which 
was studied above, is always a term, and in what- 
ever connection we may meet the phrase. Or, we 
may inquire, is it a term only when it occurs in a 
proposition? To this question we reply that terms 
are terms only in relation to the proposition in 
which they occur. For example, we may write 
down the following: 

Silver Conductor of electricity Comets 

Plants Without weight Roses 

But neither this, nor any similar list, is a list of 
terms. In logical terminology, this is a list of 
Names. By a name, therefore, we understand a 
word, or a collection of words, which has a complete 
meaning, and which may be used as the subject or 
predicate of a proposition. In the following, 'Silver,' 
'Without weight,' 'Plants,' etc., names from the 
above list, are terms : 



THE PROPOSITION 89 

Silver is a conductor of electricity. 
Comets are without weight. 
Roses are plants. 

Now it may seem that the distinction between 
terms and names is over-drawn, and that it does not 
correspond to any real difference. This is not the 
case. For observe that although the words in the 
list of names, and the words that appear in the 
propositions are the same, the meaning in the latter 
case is much more precise than in the former; it 
has changed from being vague, general, and loose, 
to being specific, particular, and fixed. In so far as 
our propositions express judgments, this is the re- 
sult that we should expect to find. For the sake 
of emphasis, the difference between a name and a 
term may be stated in the following way: 

A Name is a word, or a collection of words, with 
a complete meaning, which may be thought of as 
the S or P of a proposition. 

A Term is a word, or collection of words, with 
a complete meaning, which is thought of as the S 
or P of a proposition. 

Both terms and names are ordinarily expressed 
in words, but it is not because they are words, but 
because they have meaning that they are so called. 
Terms and names are significant words. We are 
not confined, however, to the study of words from 
the standpoint of their significance or meaning. 
Grammar, for example, studies words with respect 
to the uses they have in sentences. Substantitives, 



90 A TEXT-BOOK OF LOGIC 

verbs, prepositions, adjectives, adverbs, etc., are the 
names of various classes of words that are recog- 
nised by grammar when their use is made the basis 
of classification. Logic also finds it convenient to 
classify words with respect to their uses as terms 
in the proposition, disregarding, as does grammar, 
the meaning that particular words may have. But 
the logical classification is simpler than the gram- 
matical, because the logical requirements are nar- 
rower and more precise than the grammatical. 
Words, for logic, are arranged in two main groups, 
according as they are or are not able to stand by 
themselves as S or P in a proposition. Words which 
by themselves are capable of being thought of as S 
or P of a proposition are called Categorematic 
words. Words, on the other hand, which require the 
assistance of other words before they can be 
thought of as the S or P of a proposition are called 
Syncategorematic words. 'Metal/ 'laws/ 'elements/ 
'custom/ are categorematic words, since they may 
stand by themselves as terms in a proposition. For 
example : 

All metals are elements. 
Some laws arise from custom. 

The words 'of/ 'the,' 'always/ 'a/ in the following 
statements, are syncategorematic words, because by 
themselves they cannot be thought as S or P in a 
proposition. 



THE PROPOSITION 91 

Mistakes are not always a proof of ignorance. 
Bismarck is the man of iron. 
A burnt child dreads the fire. 

The only apparent exception to the statement of 
what should be understood by a syncategorematic 
word is illustrated by such instances as the follow- 
ing: 'Good is an adjective,' 'Of is a preposition,' 
But it should be observed that it is not the use of 
the word in a logical proposition, but the word as 
an example of a group of words in grammar that 
is the subject term of such propositions. They are 
for logic categorematic words. 

If we examine the logical classification of words, 
we shall see that the terms of propositions in which 
categorematic words occur are single-worded terms, 
while the terms of propositions in which syncatego- 
rematic words occur must necessarily be many- 
worded terms. On the basis, therefore, of the 
kinds of words that enter into them, we may 
classify terms as either single-worded or many- 
worded terms. 

The Copula. The most distinctive element of the 
proposition is the copula. It is always expressed 
by 'is' or 'is not,' 'are' or 'are not,' depending on 
whether the subject term of the proposition is sin- 
gular or plural, and whether the judgment is affirm- 
ative or negative. From the standpoint of the 
hearer, the proposition tends to fall apart into its 
terms ; and it is the function of the copula to hold 
them together in the concrete unity of a single idea, 



92 A TEXT-BOOK OF LOGIC 

and thus to preserve in the proposition a quality 
that is characteristic of the judgment itself. The 
copula must not be looked upon as a coupler be- 
tween the subject and predicate terms, nor is there 
any separate and distinct element in the judgment 
corresponding to it, and coming between the idea of 
the subject and that of the predicate. Its function 
is to express the act of judgment by which the S 
and P are really held together in the way that the 
proposition expresses. 

The copula has been a much debated subject of 
logic. It will help us to a better understanding of 
it if we consider some of the views that have been 
advanced concerning it. We may distinguish two 
such views, the relational and the existential, and 
these we shall touch upon briefly in order. 

The Relational View. This view is based upon 
the assumption that each term of the proposition 
has a distinct meaning, and it holds that the copula 
brings these terms together in the unity of a single 
statement. If we adopt this view, we are required 
to admit that our concepts or terms are independent 
of our judgments, and that is to deny that judgment 
is the starting-point of knowledge. The discussions 
of the logicians of the Middle Ages over Univer- 
sals were concerned with this subject, and they were 
divided in their opinion as to whether concepts ex- 
isted apart from our knowledge of them. The views 
developed by the Schoolmen, as the great thinkers 
of the Middle Ages were called, are three, and these 
we may enumerate and describe briefly. The real- 



THE PROPOSITION 93 

istic view, held by Anselm and Aquinas, was that 
universals or concepts have an existence before and 
independently of the particular objects through 
which we become aware of them. Briefly expressed, 
this position was summarised in the Latin state- 
ment: Universalia ante rem. The view of the 
Nominalists was that universals or concepts owe 
their existence to the prior existence of the par- 
ticular objects of our experience, or, as they said, 
Universalia post rem. This view was held, among 
others, by Roscellinus. A conceptualist view, 
which aimed to embody the truth of each of the for- 
mer views, was developed by Abelard. This view 
called attention to the fact that universals or con- 
cepts have no meaning apart from the particular 
objects in which they are embodied, and that par- 
ticular objects have no meaning apart from the uni- 
versal or concept which gives them their significance. 
These ideas are expressed in the Latin statement: 
Universalia in re. Outside the official teaching of 
the Roman Church, which is realistic, some form of 
conceptualism quite generally prevails at the present 
day. At any rate, it would be agreed by most logi- 
cians that concepts are elements of our knowledge, 
and that it is our ability to judge, — to assert like- 
nesses and differences of the objects of our expe- 
rience, — that gives existence and life to the things 
we call concepts. Psychology and logic both teach 
that the objects of our experience are inextricably 
connected, and that our knowledge grows by dis- 
tinguishing now one aspect and now another of the 



94 A TEXT-BOOK OF LOGIC 

inter-related world of men and things around us. 
If this is true, there is no object that is merely 
itself, or that exists in isolation from everything 
else. Every object with which we are in any way 
concerned is always becoming for us something else, 
showing some new quality or entering into some 
new relation. This state of affairs is expressed in 
logic by saying that there are no S's that are not P's, 
that the P predicated of any S is not a foreign thing 
that is added to it by the copula, but some quality 
that it already possesses, or some relation that it 
actually sustains. In other words, we never start 
with a bare S, with an S that is an unrelated unit, 
but with an SP that is a relational unity, and it is 
this fact that becomes explicit in the judgment, S 
is P. Unless S were already P, judgment would be 
impossible, and the proposition could not exist. The 
proposition makes explicit what is already present 
in knowledge, and since knowledge, whatever its 
form, is a qualification of an S by a P, there does 
not seem to be any separate meaning for the copula 
when knowledge is expressed in a proposition. That 
is to say, we do not need the copula for the estab- 
lishment of the knowledge relation; but it is used 
in the proposition, as Mill asserts, as "a sign of 
predication." In other words, the copula must be 
understood as serving notice upon the person who 
undertakes to interpret the proposition that S and 
P are not separate and distinct things, but, for the 
purposes for which the proposition is expressed, 
one and inseparable. The proposition, that is, does 



THE PROPOSITION 95 

not tell us about any S, but only about the S that 
is P. 

The Existential View. This view arises out of 
the fact that 'is,' besides serving as "a sign of pred- 
ication," has also a meaning of its own, namely, 
existence. Thus, if we say that, 'Aristotle is the 
father of formal logic,' it may seem that we are not 
merely stating the relation of Aristotle to the science 
of logic, but are also asserting the existence of Aris- 
totle. For if we do not believe in the reality of Aris- 
totle, what significance, it may be asked, can belong 
to the statement that he is the founder of formal 
logic? To preserve the proposition, therefore, from 
evaporating into mere nonsense, we seem forced to 
admit that the reality of the subject term must be 
secured by the structural character of the proposi- 
tion itself. Thus, if we consider the structural for- 
mula, 'S. is P,' we must, from this point of view, 
interpret it as meaning, 'S is, and it is P.' That is 
to say, the significance of the predication, 'S is P,' 
depends upon our right to take the copula twice 
over, and in each case with a different meaning. In 
the first case, *S is' is equivalent to 'S exists ;' in the 
second, 'S is P,' 'is' is "a sign of predication," in 
the sense already explained. This, in brief, is the 
existential view of the copula. 

It is evident that we can accept this view only 
if we take the copula in the same double way in all 
propositions. But this we can not do. There are 
some propositions whose terms forbid this interpre- 
tation of their copula. When, to take Mill's example, 



96 A TEXT-BOOK OF LOGIC 

we say that 'A centaur is a fiction of the poets/ 
existence is explicitly denied, but it is no less ex- 
cluded when, explaining a name, we say, 'A couch 
is an article of furniture used for reclining/ Fur- 
ther, if we say that 'Shakespeare's Henry V is nobly 
drawn/ we are obviously moving in the sphere of 
fiction, as we are moving in the realm of mythology 
when we say that 'Zeus is king of all the gods/ In 
cases like the foregoing, the existential interpreta- 
tion of the copula seems to be without meaning; 
but this is so not because 'is' has lost the meaning 
of existence, but because the terms of the proposi- 
tion will not support such an interpretation. Thus 
we see that the effort to give the copula a distinctive 
sense, over and above what it has as "a sign of 
predication/' breaks down before the controlling 
influence of the terms which constitute our proposi- 
tions. As we have seen, propositions are statements 
of the relationship of terms, and the relations are 
determined not by any special meaning carried by 
the copula, but by the character of the terms that 
enter into prepositional statements. 

To meet these difficulties, it is sometimes pointed 
out that, for speaker and hearer alike, all motive 
for judgment is taken away unless we presuppose 
the reality of the subject-matter of our judgments. 
We do not express judgments, it is said, about sub- 
jects which we believe do not exist. This may be 
readily granted ; but we should remark, at the same 
time, that it is one thing to admit that existence 
is presupposed by our judgments, and quite another 



THE PROPOSITION 97 

to affirm that reality is asserted by the copula of 
the propositions in which our judgments are ex- 
pressed. Judgments may imply reality without as- 
serting reality. Belief in the reality of Columbus, 
for example, is implied in the statement that 'Co- 
lumbus is the discoverer of America ;' but what the 
statement asserts is that he discovered America. 
And what is true of this case, is substantially true 
of every case of the judgment. 

If, then, we must hold that belief in reality is 
presupposed by every judgment, it is obvious that 
we cannot mean the same thing by existence in 
every case of judgment. In the examples, 'Utopia 
is the ideal commonwealth as depicted by More/ and 
'The sun is the centre of our solar system/ we can 
not be supposed to imply that 'The sun' and 'Utopia' 
belong to the same sphere of existence or reality. 
In other words, we must recognise different spheres 
of reality, and it is existence within one or other 
of these spheres that is implied in every judgment 
that we make. Thus, 'Utopia' belongs to the world 
of the imagination ; 'The sun' to the world of phys- 
ical objects. This is a doctrine of logical importance, 
for we may remark that ambiguity, misunder- 
standing, and error arise when what a judgment 
asserts as true within one sphere of reality is taken 
as true within another with respect to which the 
judgment has not been determined. If, for example, 
I say that 'I believe in the reality of Santa Claus,' 
I am, of course, asserting a belief which falls within 



98 A TEXT-BOOK OF LOGIC 

the world of ideas; but if you understand me to 
imply the corporeal and individual existence of 
Santa Claus, you only emphasise your misunder- 
standing of what I asserted if you challenge me to 
produce him, or to have him as my guest on Christ- 
mas Day. 

We may, then, sum up this discussion in the fol- 
lowing statements: (1) the copula does not express 
existence, but is only 'a sign of predication;' (2) 
reality of their subject-matter is presupposed — not 
expressed — by all our judgments; (3) there are 
different spheres of reality within which the mean- 
ing of our several judgments is to be determined; 
and (4) a failure to refer any judgment to its proper 
or intended sphere of reality leads to ambiguity, 
misunderstanding, and error. 

Kinds of Propositions. There are three main 
types of propositions ; the categorical, the dis- 
junctive, and the hypothetical. In this section we 
shall limit ourselves to the task of characterising 
each kind of proposition, reserving for other chap- 
ters the discussion of the logical problems which 
are connected with these forms of statement. In 
the first place, however, it should be remembered 
that we are considering propositions in general, and 
that, however the categorical, the disjunctive, and 
the hypothetical propositions differ from each other, 
they all share the common characteristics of propo- 
sitions. It is, we have seen, the business of propo- 
sitions to express the affirmative or negative rela- 
tions between the objects of our experience when 



THE PROPOSITION 99 

these relations have become explicit in judgment. 
This function of the proposition is called in logic 
'predication.' In every proposition P is predicated 
of S, and as we have seen, the copula is the sign 
of such predication. With respect, therefore, to the 
three types of proposition we may say that they 
differ, if they differ at all, by reason of the differ- 
ence in the forms of their predication. And this is 
the usual way of distinguishing them. Thus, in the 
categorical proposition we have simple predication ; 
in the disjunctive proposition, alternative predica- 
tion; and in the hypothetical proposition, condi- 
tional predication. The structural formulae for 
these three kinds of proposition respectively are: 
'S is P ;' 'S is either P or Q or M ;' 'If S is P, it is 
M.' We may also illustrate each kind by the fol- 
lowing examples : The way of the transgressor is 
hard ;' Today is either Monday or Tuesday or Wed- 
nesday or etc. ;' 'If Caesar was ambitious, he de- 
served to die.' 

Relations of the Main Types of Propositions. Prop- 
ositions have been distinguished as either categor- 
ical, disjunctive, or hypothetical. These different 
forms of proposition correspond to the different de- 
grees of certainty or explicitness of the judgments 
they express. Now, since we know more about 
same subjects than we do about others, and our 
knowledge of some parts of some subjects is more 
exact than it is about other parts, we should expect 
that this fact would be reflected in the propositions 
in which we express our several judgments. In 



100 A TEXT-BOOK OF LOGIC 

other words, the difference in the forms of proposi- 
tional statements corresponds to a difference in the 
explicitness of the knowledge asserted by our judg- 
ments. There is pretty general agreement among 
logicians as to the foregoing statement. There is 
not, however, the same harmony among them on the 
question of the precise order in which the several 
types of propositions should be arranged. We 
would suggest that they may be taken, in the order 
of their increasing exactness, in the following way : 
the disjunctive, the hypothetical, and the categor- 
ical. That is to say, the disjunctive and the cate- 
gorical propositions, respectively, express the least 
and the most explicit forms of knowledge, and the 
hypothetical, to which class most of our judgments 
belong, will appear as a form of statement that ex- 
presses, in the majority of cases, the maximum at- 
tainable certainty in our quest for knowledge. 

To consider each case separately, we may say of 
the disjunctive proposition that it expresses uncer- 
tainty as to the details of a subject-matter which is 
explicitly under consideration. For instance, we 
may not be in doubt that there will be students 
whose task it will be to read this paragraph, but 
we may not be certain how far they will understand 
it. If, in such a case, we tried to make the details 
of judgment as precise as possible, our proposition 
would then assume this form: The student who 
reads this paragraph will either understand it, or 
not understand it, or misunderstand it.' Such a 
statement, or the judgment presupposed by such a 



THE PROPOSITION 101 

statement, does not carry us far on the way to 
knowledge. It leaves us in doubt at the point where, 
if we are to have probable knowledge, uncertainty 
can not exist, namely, in respect to the details of the 
judgment's content. In other words, the disjunctive 
proposition starts with a belief in the reality of an 
S, but is uncertain as to what S is, that is, whether 
it is one or other of a number of alternatives which 
are possible of realisation in the sphere of existence 
or reality covered by S. All that, in such a case, 
we can say is that 'S is either A, or B, or C, or D.' 
If now we consider the hypothetical proposition, 
we find that the defect of the disjunctive propo- 
sition has been overcome, and we are no longer in 
doubt as to what we are asked to believe. But we 
also notice that the greater explicitness of the rela- 
tions expressed by the proposition has been secured 
by a corresponding loss. To consider the latter 
point first, we may observe that the hypothetical 
proposition does not imply, as does the disjunctive 
proposition, a definite belief in the existence of the 
sphere of reality within which the relations ex- 
pressed by the proposition are understood to fall. 
In the case cited, for instance, the disjunctive prop- 
osition started with belief in the existence of The 
student who reads this paragraph.' In the hypo- 
thetical proposition the relations involved in this 
belief are used as a condition of the ensuing judg- 
ment. Thus, The student who reads this paragraph' 
becomes, in the hypothetical proposition, 'If a stu- 
dent reads this paragraph,' — a form of statement 



102 A TEXT-BOOK OF LOGIC 

which, of course, leaves us uncommitted as to 
whether there is any such student or not. So far, 
therefore, as the hypothetical proposition is con- 
cerned, belief is never definitely implied in the exist- 
ence of the sphere of reality within which the rela- 
tions asserted by the judgment find their possible 
realisation. This, however, is not an uncompen- 
sated limitation. For, to consider the other point 
mentioned above, the meaning expressed by the 
hypothetical proposition is specific; the details with 
which the judgment is concerned have become de- 
fined in such a way that the conditions on which 
belief rests form part of what the judgment asserts. 
Thus, fully expressed, the hypothetical proposition 
reads, 'If a student reads this paragraph, he will 
understand it.' In this case the internal structure, 
the organic relations, of the elements of thought are 
more highly specialised than they are in the disjunc- 
tive proposition, and what we are told is that an 
understanding of 'this paragraph' is definitely 
grounded in the sphere of belief implied, although 
indefinitely, by the proposition itself. If we may 
hold that knowledge grows by the definition of de- 
tails, we shall have to say that the hypothetical 
proposition expresses a higher type of knowledge 
than the disjunctive proposition. 

The categorical proposition, if it exists, carries 
us outside the boundaries of probability into the 
field of certainty. The categorical proposition com- 
bines certainty as to the existence of the sphere of 
reality which is characteristic of the disjunctive 



THE PROPOSITION 103 

proposition, and certainty as to the detailed rela- 
tions of the matter of the judgment which is charac- 
teristic of the hypothetical judgment. Hence our 
proposition reads, The student who reads this par- 
agraph, will understand it.' But in order to under- 
stand the categorical proposition, we should observe 
that our knowledge of any subject-matter is so 
rarely, if ever, complete, and that, in those cases 
where it is, the material of judgment is likely to be 
so insignificant, that, from the logical point of view, 
the categorical proposition must be held to express 
either an ideal limit of knowledge, the goal toward 
which knowledge is constantly advancing but never 
quite reaches; or that it is the least serviceable, 
because least significant, form for the expression 
of truth. We may, perhaps, roughly indicate the 
meaning of this remark by the commonplace obser- 
vation that an examination of the forms of state- 
ment of the poorly educated reveals a predominance 
of categorical propositions; and, that, as we rise in 
the scale of educated intelligence, the other forms, 
and especially the hypothetical form, predominate. 
Dogmatic statements, in other words, are character- 
istic of the man who does not know, or of the man 
who knows things about which no one particularly 
cares. In either case, we should have to say that 
such statements, from the logical point of view, are 
pseudo-categoricals, that they express a belief which 
either goes beyond or falls below the range of our 
knowledge of significant reality. But this perver- 
sion of the categorical proposition by the ignorant, 



104 A TEXT-BOOK OF LOGIC 

need not obscure for us its proper logical position. 
It does express the form into which knowledge, 
when it is perfect, would naturally fall. The cate- 
gorical proposition implies belief in the existence 
of a sphere of reality within which certain ex- 
pressed relations are fulfilled. It, however, remains 
an ideal because, our knowledge being finite, we 
can never get beyond the possibility of doubt as to 
whether one or other of the conditions of the judg- 
ment has been completely satisfied. 

REFERENCES 

B. Bosanquet, The Essentials of Logic, Lect. V., VI. 

J. E. Creighton, An Introductory Logic, 3d Edition, Ch. VI. 
J. G. Hibben, Logic, Deductive, and Inductive, Ch. IX. 
S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
tion, Ch. IV. 
W. Minto, Logic, Inductive and Deductive, Part III., Ch. I. 

C. Read, Logic, Deductive and Inductive, 3d Edition, Ch. II. 

ADVANCED 

J. M. Baldwin, Thought and Things, Vol. II., Part II., Ch. VI. 

W. R. B. Gibson, The Problem of Logic, Chs. IX., XI., XII. 

H. W. B. Joseph, An Introduction to Logic, Ch. VII. 

J. S. Mill, A System of Logic, Book I., Ch. IV., 1, V., VI., 5. 

F. C. S. Schiller, Formal Logic, Ch. IX. 

C. Sigwart, Logic, Vol. I., Part I., 5, Ch. II., 17, VII. 

J. Welton, A Manual of Logic, Vol. I., Book I., Ch. I. 

QUESTIONS 

1. In what respect does the proposition differ from the 
judgment? 

2. What is meant by the import of a proposition? 



THE PROPOSITION 105 

3. Distinguish between the truth-import and the statement- 
import of propositions. 

4. What light does this distinction throw upon the inter- 
pretation of propositions? 

5. Why do we always write the subject term of a proposi- 
tion first? 

6. How may we distinguish between the subject and pred- 
icate terms, and is it always possible to make this dis- 
tinction? Explain. 

7. What is the logical difference between terms, names, 
and words? 

8. Give a logical classification of words. 

9. What is meant by single-worded and many-worded 
terms? 

10. What is meant by saying that the copula is the most 
distinctive element of the proposition? 

11. State and criticise the relational view of the copula. 

12. What are the realistic, nominalistic, ana conceptualistic 
views of the concept? 

13. What is the existential view of the copula, and what 
objections can be brought against it? 

12. What do you understand by predication? Characterise 
the various kinds of predication, and show how these 
give rise to the several types of logical proposition. 

15. What are the conditions under which we give a disjunc- 
tive expression to our judgments? 

16. Discuss the nature of hypothetical propositions, and 
show their relation to disjunctive propositions. 

17. Discuss the nature and limits of categorical proposi- 
tions. 

EXERCISES 

1. Illustrate, from your own observation preferably, the 
possibility of confusing the truth-import with the state- 
ment-import of a proposition. 

2. Write the following sentences in the form of proposi- 
tions, indicating the subject and predicate terms in 
each: 



106 A TEXT-BOOK OF LOGIC 

(1) Over the mountains poured the barbarian horde. 

(2) The moonlighh plays fitfully upon yonder rippling 
stream. 

(3) Happy is the man that findeth wisdom. 

(4) All is not misfortune that seems at the moment un- 
endurable. 

3. Write six sentences in which you think it difficult or im- 
possible to distinguish the subject and predicate terms. 

4. Make a list of twelve categorematic words. 

5. Write six statements which show the error of an exist- 
ential interpretation of the copula, and explain the rea- 
son in each instance. 

6. Write disjunctive propositions about the following sub- 
jects : 

(1) Your presence at a concert to be given, say, next 
week. 

(2) The result of a particular political election. 

7. Write hypothetical propositions about the following sub- 
jects: 

(1) Tomorrow's weather. 

(2) The study of the biological sciences. 



CHAPTER IV 
TERMS 

Proposition and Terms. In the last chapter, we 
defined a proposition as the verbal expression of a 
judgment in which something (P) is predicated of 
something else (S). We also analysed the propo- 
sition into its constituent factors — terms and the 
copula — and saw that the relation which these ele- 
ments sustain to one another is determined by the 
meaning of the proposition taken as a whole. The 
proposition, that is to say, was considered as deter- 
mining the existence and character of its terms, and 
not the existence and character of terms as deter- 
mining the existence and character of the proposi- 
tion. Terms are different aspects of the meaning 
of the proposition in which they occur. Expressed 
otherwise, they are functions of their propositions. 
The further discussion of terms which we begin in 
this chapter must be carried on in light of these 
general positions, and it must be considered as a 
more detailed consideration of certain important 
features of the proposition. The separate chapter 
headings are employed merely for pedagogic con- 
venience. 

Connotative and Denotative use of Terms. We are 
to consider at the outset a distinction in the use of 
terms upon which hinge many of the problems that 
will come before us in the succeeding pages. It is, 

(107) 



108 A TEXT-BOOK OF LOGIC 

therefore, important to give special attention to the 
precise logical significance that the distinction has, 
and to get clearly before ourselves the scope of its 
application. The latter point will be discussed in 
the next section; we shall, therefore, confine our- 
selves here to a statement and illustration of the 
uses — connotative and denotative — to which terms, 
whatever their character, may logically be put. 

It is part of our common knowledge that words 
are frequently used as labels by means of which we 
identify things, and distinguish these things from 
other things. Many illustrations will come to mind : 
'the Rocky Mountains/ 'the Amazon River,' 'my old 
bay horse,' etc. There is hardly any end to the 
number of words which have this use of pointing 
to objects, and which put us in contact with par- 
ticular things, or groups of things. Now it is this 
fact of our common speech that logic describes when 
it talks about the denotative use of terms. Terms 
are used to point out, refer to, or indicate objects. 
For instance, in the statement, 'When it comes to 
packing, books are a nuisance,' the term 'books' re- 
fers to the individuals of a class of objects, and it 
is, therefore, said to be used denotatively. In the 
same way, the term 'lion' in the proposition, 'Lions 
are carnivorous animals,' is used to point out this, 
that or the other particular lion, and the proposition 
means that any individual lion will be found to 
possess the specified characteristics. Since the term 
'lion' points out the individual objects one has in 



TERMS 109 

mind when the term is used it is said to be used 
denotatively. 

We may also go to our ordinary employment of 
language to ascertain what logic understands by the 
connotative use of terms. Words, as we know, not 
only point out objects, but they also have meanings. 
When, for example, we hear a strange word spoken, 
or meet with it in our reading, we ask what the 
word means. If no one can tell us, we go to the 
dictionary for the information. Now we do this, 
because we have been trained to expect that the 
words we meet will arouse some sort of mental 
image, and because experience has taught us that, 
when they do not, we fail to understand what is 
said to us. That words should have a meaning is 
just as important as that they should indicate indi- 
vidual objects. Unless such words as Violin,' 'art/ 
'mathematics,' 'landscape,' 'ocean' aroused within us 
quite different images or ideas, we should be at a 
loss how to use them, or to understand them. Now 
logic indicates this aspect of words, their meaning 
aspect, when it speaks of the connotative use of 
terms. Terms, from this point of view, are used to 
call up the qualities or attributes of objects. When 
we use a term connotatively, it must be understood, 
consequently, that we are speaking about its dic- 
tionary meaning. But, it should also be observed, 
the particular dictionary meaning of any term can 
be determined only from the standpoint of the par- 
ticular proposition in which the term occurs. For 
example, in Shakespeare's Coriolanus we read, 'She 



110 A TEXT-BOOK OF LOGIC 

will but disease our better mirth/ a passage in 
which the term 'disease' means 'disturb/ When 
Locke writes, 'Although great light be insufferable 
to our eyes, yet the highest degree of darkness does 
not disease them/ he is using the same word in the 
sense of 'cause suffering to/ When, further, in 
Thomson's Summer we read, 

Then wasteful forth 
Walks the dire power of pestilent disease, 

'disease' is used in the more usual sense of 'a phys- 
ical or physiological disorder.' This dependence of 
the meaning of terms on their propositions is of 
capital importance, and should be kept constantly 
in mind. 

Relation of the Connotative and Denotative use 
of Terms. The difficulty that is usually experienced 
in understanding the doctrine of connotation and 
denotation is due to the fact that we do not have 
one group of words whose use is always connota- 
tive, and another group of words whose use is 
always denotative. Most, if not all, terms are capa- 
ble of being used in either the one or other of these 
ways. But this is not all. The most important 
fact to remark is that in whichever of the ways 
mentioned a given term is employed, it is so em- 
ployed with the other use more or less distinctly 
in mind. It would be quite a fair statement of the 
case to say that there is always a reference of the 
one to the other, and that in any particular instance 
the one implies the other. It is not difficult to see, 



TERMS 111 

for example, that the identification of the individ- 
uals which are denoted by any term depends upon 
their possession of the qualities that are connoted 
by the same term. It is also clear that the qualities 
that a term connotes are the qualities of the individ- 
uals which the term denotes. Let us, for example, 
examine the subject term of the proposition, 'Man 
is a rational animal.' If the term 'man' is used 
denotatively, that is, to point out Tom, Dick, 
Harry, etc.,' the proposition must mean that 'Tom, 
Dick, Harry, etc.,' are the individuals in whom are 
found realised the qualities expressed by the pred- 
icate term. If the term 'man' is used connotatively, 
the proposition must mean that the qualities, 'ra- 
tional animal,' will be found present in each indi- 
vidual, that is, in 'Tom, Dick, Harry, etc' Let us 
take, as another case, 'Man is a being who volun- 
tarily sets himself tasks.' If, in this proposition, 
the term 'man' is used to denote individual men, 
then our identification of the individuals who set 
themselves tasks depends upon our knowing what 
the qualities are which the term 'man' connotes ; and 
if it is used to connote certain qualities, our under- 
standing of the proposition depends upon the sup- 
position that these qualities can be found in a num- 
ber of discoverable individuals. These illustrations 
serve to emphasise the general rule that the con- 
notative use of a term does not break away entirely 
from its denotative use, or vice versa; and the sole 
logical distinction between them is that, in the one, 
we lay the primary emphasis on the individuals 



112 A TEXT-BOOK OF LOGIC 

which possess the qualities, and, in the other, on the 
qualities possessed by the individuals. 

Another inquiry which comes before us here is 
whether this relation between the connotative and 
the denotative use of terms is realised in all terms 
whatsoever. We can give an answer to this ques- 
tion only by anticipating certain features of the dis- 
cussion of terms contained in the following pages. 
We may, however, at this point call attention to the 
generally accepted position that no term is ever so 
exclusively denotative as to lose all connotation 
whatsoever, and that no term can be said to have 
developed on the side of meaning, i. e., connotatively, 
so one-sidedly as to have lost all reference to objects. 
The discussion of this question has been brought to 
the study of proper names as to a test case ; and it 
is thought that if the position can be maintained 
with respect to these terms, it will be possible to 
maintain it with respect to other kinds of terms. 
The question is not a theoretical one, and we shall 
gain nothing by considering it as such. It is a 
question of fact, and can be determined only by a 
study of each kind of terms as it comes before us 
in this and the following chapter. We may express 
the opinion, however, that it is quite possible that, 
in the course of time, the employment of particular 
terms may shift from a predominantly connotative 
to a predominantly denotative use, and there is no 
reason, except one of convenience, why all meaning 
should not drop away from some terms, and that 
they should stand in our vocabulary merely as sym- 



TERMS 113 

bols of the existence of things. Whether there are 
any such terms cannot be decided now; it is more 
important to see that the possibility of this being 
the case does not obscure for us the more general 
relation which was expounded in the preceding para- 
graph. 

A subject that is usually discussed in this con- 
nection relates to the changes that take place in the 
connotation and denotation of terms when either 
of these is increased or decreased. Under these 
conditions, the changes in the connotation and deno- 
tation of terms are said to vary inversely. More 
fully stated, when the connotation of a term is in- 
creased, its denotation is decreased, and vice versa. 
For example, the denotation of the term 'man' is 'the 
total population of the earth,' and its connotation, 
we may say, is 'rationality and the upright position.' 
If we increase the connotation by specifying 'white 
man,' the connotation of which term is 'white, ra- 
tionality and upright position,' we decrease the de- 
notation which then refers to 'the white population 
of the earth.' If a further increase in connotation 
is made by specifying 'European white man,' the 
denotation is decreased still more, and indicates 'the 
white population of Europe.' The process thus 
begun can be carried as far as interest or ingenuity 
allows. The general truth to which such illustra- 
tions point is that the denotation of a term is dimin- 
ished as its connotation is made more definite by the 
addition of new attributes; and, conversely, that 



114 A TEXT-BOOK OF LOGIC 

when the connotation is decreased by dropping at- 
tributes the number of individuals to which the 
term applies is increased. This statement holds 
good as a general rule, but there is no numerical 
ratio between the increase or decrease of connota- 
tion and the accompanying decrease or increase of 
the denotation. Indeed, the denotation of a term 
may be increased greatly without any change in its 
connotation, as actually happened, for example, 
when the British government annexed some mil- 
lions of Africans at the close of the Boer war with- 
out making thereby any change at all in the conno- 
tation of the term, 'British subject.' 

Distribution of Terms. If we carry our study of 
the denotative use of terms a step further, we shall 
find that the purposes which prompt our statements 
sometimes require us to refer to a determinate num- 
ber of the individuals denoted by the term, and that 
sometimes our purpose is satisfied if we indicate 
an indeterminate number of the individuals included 
under the term. Let us suppose, for example, that 
we are discussing the theory of kingship, and that 
I express the belief, after Hobbes, that the king can 
do no wrong. If this belief were thrown into a 
propositional form, it would become clear that I am 
thinking of all the individuals who have exercised, 
or at some time may exercise, the functions of king- 
ship. What I mean is that 'No king can do any 
wrong/ that is, wrong doing cannot be predicated 
of any king, — of this, that, or of any other indi- 
vidual who is or may be a king. If such a state- 



TERMS 115 

ment does not recommend itself to your judgment, 
and you express dissent from it, you are not re- 
quired, by the conditions of the situation which 
determine your judgment, to concern yourself with 
each and every king; it will be sufficient, if wrong 
doing by kings has ever occurred, for you to limit 
your statement to any of the cases which contradict 
the theory you oppose. Expressed in a proposition, 
your judgment will be 'Some kings can do wrong/ 
or more definitely, 'Some kings have done wrong.' 
You are obviously speaking of a number of indi- 
viduals, not definitely specified, who belong to the 
group denoted by the term 'king.' The distinction, 
thus indicated, in the denotation, width, or extent of 
terms, is known in logic as the 'distribution' of 
terms. By the distribution of terms we mean the 
consideration of terms from the standpoint of their 
quantity. Now, in respect of quantity, we are lim- 
ited in logic by the contrast between a definite and 
an indefinite number, and the terms which denote 
these quantities are said to be distributed and un- 
distributed respectively. A term is 'distributed' 
when, from the form of the proposition in which it 
occurs, it is known to refer to a determined number 
of individuals of the class denoted by the term; it 
is said to be 'undistributed' when, from the form 
of the proposition in which it occurs, it is known 
to refer to an undetermined number of the individ- 
uals of the class denoted by the term. The tech- 
nical sign of a distributed term, in an affirmative 
proposition, is 'All,' and, in a negative proposition, 



116 A TEXT-BOOK OF LOGIC 

'No.' The technical sign of an undistributed term, 
in both affirmative and negative propositions, is 
'Some.' 

We have just said that the difference between 
distributed and undistributed terms is that in 
undistributed terms the exact number of in- 
dividuals referred to is left indefinite, as, for 
example, 'Some birds are blue;' while in distributed 
terms the number is made definite, as for example, 
'No man is free from the defects of his qualities,' 
and 'Half my goods I give to feed the poor.' We 
shall have occasion to discuss this distinction again 
when we study the interpretation of propositions; 
but for the present, it is enough to remark that 
neither in the case of a distributed, nor in that of 
an undistributed, term can we say, from the form 
of the proposition, what the arithmetical number 
of the individuals denoted by the term is. It may, 
perhaps, help to make the matter clear if we recall 
that in the study of algebra we are taught to use 
the first letters of the alphabet, a, b, c, to represent 
the known quantities of a problem, and the last let- 
ters of the alphabet, x, y, z, to represent the un- 
known quantities. The mathematical difference be- 
tween these two classes of quantity, the known and 
the unknown, is the difference between the dis- 
tributed and the undistributed use of terms in logic. 
In the former case, the known objects are deter- 
minate; in the latter, the unknown objects are inde- 
terminate. 



TERMS 117 

Some other Characteristics of Terms. In the fore- 
going paragraphs, we have considered mainly those 
features of terms which are important from the 
point of view of their denotation. There are cer- 
tain questions which arise from the standpoint of 
the connotation of terms to which we shall direct 
attention in the remainder of this and in the fol- 
lowing chapter. The questions to which we refer 
must not be confused with those that will engage 
us in a later chapter, and which relate particularly 
to the problem of definition, that is, to the problem 
of how the meaning of terms receives logical formu- 
lation. What, rather, we have to consider at pres- 
ent is the fact that there are certain general charac- 
teristics of terms which do not depend upon the par- 
ticular meaning that terms have, but upon the 
nature of the interest which stimulates our judging 
activity. The interests under which we are led to 
judge any subject-matter may require us to express 
what we wish to say either concretely, abstractly, 
absolutely, relatively, positively, or negatively. 
That is to say, our meaning may be either concrete, 
abstract, absolute, relative, positive, or negative. 
These distinctions are not coordinate, and they are 
not at all of equal importance; but the particular 
relations which they sustain to one another become 
apparent only when it is clear what each signifies. 
We shall, therefore, confine ourselves, in the main, 
to stating how each of these distinctions is to be 
understood, and we shall begin with the broadest 



118 A TEXT-BOOK OF LOGIC 

among them, the distinction between concrete and 
abstract meaning. 

Concrete Meaning. One of the most familiar 
facts of our every day life is that we distinguish 
from one another the various objects that come 
under our observation. When, for example, we go 
into the city, we perceive the houses, the shops, the 
traffic on the streets, and the people on the side- 
walks as quite different things. We also carry over 
into our academic studies the endeavor to make dis- 
tinctions, and to regard different things as different. 
Thus, the student of zoology learns to discriminate 
between the blood vessels, the supporting tissue, and 
the characteristic cells of the specimens he observes 
under the microscope. Indeed, so general and im- 
portant is this ability on our part that there is no 
interest that is not served by it, and no limit to 
which it may not be carried. For instance, we may 
mark off in this way not only the objects of the 
material world, but the qualities and relations of 
these objects, and set them before us as distinct ob- 
jects of our thought. Thus, 'green/ 'heavy,' 'but,' 
'cause,' may become for us objects as distinct as are 
the chairs and tables of our domestic life. Now 
whatever we set off as a distinct object of percep- 
tion or thought is in logic considered as a concrete 
object, and the term that denotes such an object is 
called a concrete term. 

It may be observed that the significance for logic 
of the term concrete depends upon the significance 
of the word 'thing' in the body of our common 



TERMS 119 

knowledge. By a thing we ordinarily mean some 
part of the physical world which is perceived as dis- 
tinct from other parts with which it coexists. Thus, 
the pictures on the walls of our room, the articles 
on display in the shop widows, the mountains and 
streams of the landscape, the cattle on a thousand 
hill, are all called 'things' whenever we think of them 
as distinct from other objects with which they are 
associated in the same common environment. But 
the word 'thing' is not confined to objects of the 
material world. We also designate as things what- 
ever can be thought of as having a distinct exist- 
ence of any kind. Thus, if I am trying to recall 
something in particular that has been told me, I may 
express my impatience at not being able to do so by 
saying, 'Why can't I remember the thing?' What I 
refer to here as a' thing is an idea. A similar usage 
is found in the commandment against idolatry 
among the Hebrews when it is forbidden them to 
make a graven image "in the likeness of any thing 
in the heavens above," where the word 'heavens' 
has a quasi-spiritual meaning. Instances might be 
multiplied of the very wide and varied use to which 
we put the word thing in popular speech, but those 
given are enough to emphasise the connection be- 
tween it and the logical meaning of the term con- 
crete. 

While, however, there is this general connection 
between the two words, the meaning of the term 
concrete is more precise than is the meaning of the 
word thing. It is true, for instance, that we do not 



120 A TEXT-BOOK OF LOGIC 

ordinarily refer to persons as things, but logic 
would have no hesitation in calling the terms, by 
which they were denoted, concrete terms. On the 
other hand, we should describe as a thing any object 
of which we could say only that it was in our con- 
sciousness, but unless we knew some of its attri- 
butes or relations, we should not be warranted log- 
ically in calling it a concrete object, or the word 
used to denote it a concrete term. These cases are 
suggestive of the truth that it is not mere existence, 
but significant existence that logic, in the main, de- 
notes by the term concrete. Whenever an object is 
thought of as having a definite kind of existence, 
that is, as possessing certain qualities or standing 
in such and such relations, it is called a concrete 
object, and the words we use to denote such objects 
are concrete terms because they are used to connote 
these qualities and relations. There are, as we shall 
see, varying degrees of definiteness in the ways in 
which significant existence is asserted, and there 
are, consequently, several degrees of explicitness in 
the meaning of the terms used for denoting such 
existence. This matter we shall discuss in the fol- 
lowing sections; it will be sufficient, meanwhile, if 
the broad meaning of the term concrete has been 
made clear. 

Individual Meanings: Proper Names and Desig- 
nations. The first class of concrete terms that we 
shall consider is that which denotes particular indi- 
vidual objects. To be able to point out individual 
objects, we must have in mind, as a general rule, 



TERMS 121 

some attribute, or group of attributes, which is 
thought of as belonging to the one object we desire 
to single out, and to make the subject of further 
consideration. The names of such objects, when 
they are used as terms in a proposition, are definitely- 
denotative and explicitly connotative ; they point to 
their objects by means of the attribute or attributes 
which the term connotes. Such terms are called 
individual, or singular, terms. 

Individual concrete terms are of two kinds: 
proper names and designations. A proper name, to 
consider that first, is the name given to an object — 
person, place, or thing — as a special means of dis- 
tinguishing this object from all other objects. We 
give names to the members of our families, — Tom, 
Dick, Mary, Sue, etc., to continents, mountains, 
rivers, towns etc. We also give names to the horses 
in our stables and the cattle in our barns. There 
is no limit, except its usefulness, to the process of 
naming the objects of our acquaintance in order to 
distinguish them from others with which we do not 
wish them confused. In all such instances the 
names are proper names, and they serve to individ- 
ualise the particular objects to which they belong. 
When such names are made the subject of pred- 
ication they are singular or individual terms. 

Now, about proper names, as thus defined, we 
may ask whether their designation of particular 
objects is made possible because they imply an attri- 
bute or attributes, that is, because proper names 
are connotative. In answer to this question, Mill, 



122 A TEXT-BOOK OF LOGIC 

for example, replied that proper names are non- 
connotative, they can be used only, he said, to sig- 
nify an subject. This is, in many quarters, consid- 
ered an extreme position, and it may be due to the 
failure to see that significance may belong to a sub- 
ject not only because of the qualities that it pos- 
sesses, but also because of the relations in which it 
stands. 'The very fact/' as Creighton points out, 
"that a proper name is given to an object implies 
that is possesses a certain marked individuality," 
and the intelligent use of the name surely implies a 
reference to the qualities or relations by which that 
individuality is defined. However, be that as it may, 
we may admit that the connotation of proper names 
is ordinarily quite general and often vague, without 
thereby refusing to grant them any significance 
whatever. If the application of such terms is un- 
ambiguous, it is quite natural that their meaning 
should drop into the background of consciousness; 
but if its application should become uncertain or be 
misunderstood, we should then feel the need of mak- 
ing the connotation of the term more definite. 

Individual concrete meaning may be expressed, 
in the second place, by a designation. Logic regards 
as a designation any phrase that describes an object 
by its qualities or relations, when such phrase is 
used for the purpose of definitely pointing out this 
object. The assassin of Franz Ferdinand of Aus- 
tria,' 'my winter overcoat/ 'the centre of the mate- 
rial universe,' 'my partner,' — all these are designa- 
tions in the sense defined. It is clear that a desig- 



TERMS 123 

nation depends upon the appropriateness of the de- 
scription it embodies for the accurate identification 
of the object to which it points. That is to say, a 
designation must be explicitly connotative as well as 
definitely denotative. 

The wide usefulness of this method of express- 
ing our individual concrete meanings is very evi- 
dent. It is true that, in ordinary life and in scien- 
tific pursuits, we need a number of terms which 
shall have the specialised function of designating 
particular individual objects, that is, terms that are 
definitely proper names. But neither in science nor 
in daily life is it necessary to assign proper names 
to all the objects that engage attention, and yet 
some method of referring to these objects is neces- 
sary if we are to develop the interests that prompt 
us to take note of them. It is under such circum- 
stances, as a general thing, that the designation 
becomes of use. We should be on our guard, how- 
ever, against supposing that the objects to which 
proper names are assigned are necessarily of more 
importance than those to which we refer by means 
of designations. While it is true that some of the 
objects which we denote by designations are rela- 
tively insignificant, this is not always the case. In 
science, for instance, we speak of 'the law of grav- 
itation,' 'the law of diminishing returns,' 'cen- 
trifugal force,' etc.; and in daiy life we use such 
phrases as 'the President of the United States,' 'the 
Secretary of State,' etc. These phrases are, accord- 
ing to the definition, designations; they point out 



124 A TEXT-BOOK OF LOGIC 

definite objects by means of a brief description of 
the objects' characteristics. They have, moreover, 
a higher importance than some of the objects to 
which proper names are given. 

General Meaning. The second class of concrete 
terms, which we have now to consider, is character- 
ised by the fact that the meaning conveyed by such 
terms is applicable to more than one object. Now, 
it is true that, if we were to list all the attributes 
of all the objects of our acquaintance, it would be 
found that no one object possessed in every respect 
precisely the same qualities as any other. Every 
object, in this sense, is a unique object; and, if there 
were no other interest in things than that which 
leads to the observation of their uniqueness, we 
should have to use, when speaking of such objects, 
either proper names or designations. It frequently 
happens, however, that our practical or theoretical 
interests require us to distinguish among the attri- 
butes of individual objects those that belong to 
only one individual, and those that are possessed in 
common by a number of individuals. On the basis 
of this distinction, we are able to group together 
the objects which possess a common set of attri- 
butes, and, conversely, to make the common attri- 
butes the basis of our inclusion of other individuals 
within particular groups. For example, we classify 
certain animals as quadrupeds, and certain others 
as bipeds, on the ground that, amid an indefinite 
number of differences, cerlain animals are alike in 
the fact that they walk on four feet, and that cer- 



TERMS 125 

tain others are alike in the fact that they walk on 
two feet. Stated otherwise, in constructing such 
classes of objects, each of the individuals belonging 
to any one class is thought of as possessing exactly 
the same characteristics as any other individual of 
that class. 

Now the names which embody a meaning that 
can be applied to any one of an indefinite number of 
individuals are known in logic as 'general' or 'com- 
mon' terms. Of such terms we may say, in view of 
the foregoing discussion, that they are explicitly 
connotative, but indefinitely denotative. In other 
words, the attributes that a general term connotes 
belong equally to each and every individual of a 
group; but we cannot tell which one or more of 
these individuals is denoted, merely by knowing the 
connotation of the term. The characteristic fact 
about a general term is, then, that while its conno- 
tation or meaning is concrete, its application is 
always general; the meaning, that is to say, can be 
applied to an indefinite number of individuals. It 
should be observed, however, that the meaning of 
any such term does not exist apart from some or 
all of the individuals in which this meaning is con- 
cretely embodied. That is to say, it is the existence 
of the individuals which form the group that deter- 
mines the meaning that any general term may have. 
Apart from these individuals, indefinitely denoted 
though they are, the general term would lose all its 
meaning. One reason for remarking this fact is 
that the interest, which leads us to observe the com- 



126 A TEXT-BOOK OF LOGIC 

mon characteristics of numbers of objects, is an 
interest that still recognizes the differences that 
exist among the objects which it groups together. 
When, therefore, these common characteristics are 
expressed in general terms, it is not to be supposed 
that the differences that distinguish one object from 
another are thereby denied. What our general 
terms imply is that the presence of individual dif- 
ferences is not inconsistent with the possession, by 
a number of objects, of certain characteristics in 
common. 

Collective Meaning: Individual and General. We 
have traced the development of meaning from the 
singular concrete to the general concrete, and we 
have seen that, in this development, we have been 
concerned with some feature or features of the indi- 
vidual or individuals which our interests prompt us 
to study. For instance, our interest in the differ- 
ences that exist between one object and another is 
embodied in the meaning that singular terms have ; 
our interest in the likenesses which exist along with 
these individual differences is expressed in the mean- 
ing that general terms have. That is to say, the de- 
velopment of meaning which leads from the individ- 
ual to the general term has been guided by the con- 
sideration that we must not do violence to the differ- 
ences that exist between one individual and another 
while seeking for the common ground of their like- 
ness. We have now to consider whether, neglecting 
the differences between individuals, we may start 
with their common likeness, and carry the develop- 



TERMS 127 

ment a step further. Or, to state the inquiry more 
definitely, we may ask what alteration in our mean- 
ing is made if and when, in our study of individuals, 
we ignore their differences, and take note only of 
their likenesses. We have seen that we may take 
account of both likenesses and differences, and still 
be able to define a meaning which applies to each of 
a number of otherwise dissimilar individuals. What 
we have now to see is that if we pay attention only 
to likenesses, or, what amounts to the same thing, 
consider only similar individuals, we are able to de- 
fine a meaning which applies to no one of the indi- 
viduals, but can be intelligently used of all these in- 
dividuals taken together as a whole. To illustrate, 
let us suppose that we bring together in one place 
a number of animals — lions, tigers, elephants, 
jaguars, ibexes, zebras, etc. Such a collec- 
tion we should call a menagerie. If, again, 
we were to bring together a number of children 
for the purpose of educating them we should 
call such a collection a school. There are many 
such collective groups of individuals; and we 
can say that the meaning of the word by which each 
is indicated applies to none of the individuals which 
constitute the group, but only to the group which is 
constituted by the individuals. Thus, 'a menagerie' 
is the name for a particular group of animals, 'a 
school' is the name for a particular group of chil- 
dren under instruction ; 'the United States of Amer- 
ica' is the name for a particular group of political 
organisations, etc, 



128 A TEXT-BOOK OF LOGIC 

Now a name which embodies a meaning that 
can be applied to a number of similar individals, 
taken together and thought of as a whole, is called 
in logic a collective term. It is obvious, from what 
has been said, that the connotation or meaning of 
collective terms is determined for us by the points 
of observed similarity between the individuals which 
constitute the groups which these terms denote. 
Thus, we call a particular group of individuals a 
nation when we think of all the individuals belong- 
ing to the group as citizens, — citizenship is the one 
attribute that all have in common. We call another 
particular group of individuals a legislature when 
we think of all the individuals belonging to the 
group as makers of laws, — making laws is the one 
common task in which all its members are engaged. 
The same thing, mutatis mutandis, will be found 
true of all collective terms whatever: the connota- 
tion of such terms embodies certain observed sim- 
ilarities between the individuals which belong to the 
groups which the terms denote. 

When, on the other hand, we consider the deno- 
tation of collective terms, it is evident that the 
groups which such terms point out constitute a new 
kind of individual, and must be distinguished from 
the individuals which are denoted by the general 
term. The individuals which general terms, as a 
rule, denote are objects of our ordinary perception 
and thought; they are the things which, in the 
course of our daily life, we are accustomed to take 
as distinct objects; such things, we may say, as 



TERMS 129 

each of us has been trained to observe in the course 
of the education that the community provides. On 
the other hand, the individuals which collective 
terms denote are individuals of a higher order, so 
to speak; they result from a definitely conscious 
effort on our part to bring together under a single 
view a number of diverse things, and to regard these 
things as one object. The objects which collective 
terms denote are more complex than those denoted 
by the general term, and should be carefully dis- 
tinguished from the latter. 

Collective concrete terms may be either individ- 
ual or general. The individual collective term is 
used to point out a particular group of objects which 
we wish to distinguish from all other objects what- 
ever. 'The Rough Riders,' 'the Gordon Highlanders,' 
'the Allies,' (in the present war in Europe) are 
examples of collective terms used in this way. It 
may be observed that the individual collective term 
always contains the definite article, 'the,' as part of 
its verbal form. Thus, 'the committee,' 'the library,' 
'the family' are collective terms used to point out 
particular distinctive groups. The denotation of 
these terms is definite. The general collective term 
is used to indicate a particular kind or class of 
grouped objects, and, therefore, may be applied to 
any particular group of objects which has the char- 
acteristics of the class which the term denotes. For 
example, when the military and naval forces of two 
or more nations act together for the purpose of de- 



130 A TEXT-BOOK OF LOGIC 

feating a common enemey, these nations are called 
allies. 'Allies' is a collective term, and, in this case, 
is general, since we apply the same name to each of 
the many combinations of this character which his- 
tory records. Other illustrations of collective terms 
which have a general application are, 'family,' 'li- 
brary,' 'committee.' 

It is sometimes said that the individual collective 
can be changed into a general collective term by 
substituting the indefinite article, 'a,' for the definite 
article, 'the ;' or by omitting the article without sub- 
stitution. Thus, 'the allies,' which is an individual 
collective term, becomes a general collective term 
by omitting 'the;' 'the committee,' 'the family,' 'the 
library' become general by substituting 'a' for 'the' 
in each instance, — 'a committee,' 'a family,' 'a li- 
brary.' Sometimes, however, the connotation of a 
collective term has become so highly specialised that 
it is capable of being applied to only a single object, 
and in that case it cannot be used, by any change 
whatever, as a general term. Examples of this are : 
'the Congressional Library at Washington,' 'the 
family of King George IV,' 'the Committee on For- 
eign Relations in the Sixty-third Congress.' 

Abstract Meaning. In the foregoing sections, we 
have studied how concrete meaning develops, and 
have seen that such meaning may assume one of 
three forms, or, as we may say, indicate one of 
three kinds of objects : — individual, general, or 
collective. We have said that, in these instances, 
the meaning is concrete because, in each of them, 



TERMS 131 

the connection between attribute and object is 
particularly direct and intimate, although the con- 
nection is in differing degrees of intimacy. Any 
meaning is considered concrete which conveys the 
idea that 'these are the attributes which such or 
such an object has,' or that 'this is the object which 
has such or such attributes.' It has been shown 
that the object, in some instances, is a material ob- 
ject; in others, it is mental. But so long as the 
meaning we wish to express is concrete, we always 
suppose that we can pass from object to attribute, 
or from attribute to object, without a break, or that 
the connection between attribute and object is un- 
equivocal. In other words, whenever we take an 
object in connection with its attributes, or think of 
attributes only in connection with their objects, our 
meaning is concrete. If, however, we were to con- 
sider attributes apart from objects, we should con- 
front a new situation, and one which would involve 
a new set of problems, the consideration of which, 
in the end, would lead us to define a new kind of 
meaning which, in contrast to concrete, might ap- 
propriately be called 'abstract.' For by abstract 
meaning we commonly understand the idea of an 
attribute — quality or relation — thought of inde- 
pendently of the particular object or objects of 
which it is the attribute. 

Now, when we look at the possibility of the ex- 
istence of such meanings as this, we are confronted 
with the danger of meaning less than we actually 
say. For instance, some logicians have defined the 



132 A TEXT-BOOK OF LOGIC 

terms in which our abstract meanings are expressed 
— 'abstract terms,' as they are called — as those 
which apply to objects thought of apart from the 
whole to which they belong, or to attributes which 
are thought of apart from the objects of which they 
are the attributes. Thus, a 'leaf thought of apart 
from the tree on which it grows is, according to this 
definition, an abstract term, and 'green,' if it is not 
thought of as the color of this particular leaf, or of 
any other particular green object, is likewise an 
abstract term. In our view, this is a very mislead- 
ing statement of what abstract meanings and terms 
are. For instance, in the cases just mentioned, both 
'leaf and 'green' are concrete general terms. The 
one is the name of an object, the other of an attri- 
bute, and although these terms are not thought of 
as belonging to any one particular object, still they 
are thought of as belonging to any one of an in- 
definite number of particular objects; unless we 
think of them in this way we cannot think of them 
at all. But if this is what we are to understand by 
an abstract term, then abstract are not distinct 
from general terms, and have to be classed as such. 
Although the view we have just criticised is apt 
to be misleading if it is taken as providing a defin- 
ition of what abstract meaning is, it may neverthe- 
less serve a useful purpose if it indicates how such 
a meaning is developed. It is true that in order to 
make our meanings abstract, we have to take attri- 
butes and objects apart from their mutual impli- 
cation of each other; but merely to take objects or 






TERMS 133 

attributes in isolation is not, in itself, sufficient to 
secure a new logical product. The difficulty of such 
a view as we are criticising can be seen if we 
observe what would follow from its acceptance. 
For if, according to this view, only a meaning 
were retained, the thing meant by it being ig- 
nored, we may ask about this meaning whether 
it is a detached meaning, — a meaning that is not 
the meaning of any object. If we answer this ques- 
tion in the affirmative, as we are required to do, we 
have opened the door to all the absurdities that be- 
long, in the popular understanding of the word, to 
'abstract' thought, — to thought, that is, that has 
nothing to do with any definable reality. To illus- 
trate, if from a student who comes for the first time 
to the study of philosophy, we were to elicit by care- 
ful questioning what his uninstructed understand- 
ing of philosophy is, we should probably find that 
for him philosophy is a set of ideas more or less 
connected with one another, but having little or no 
connection with anything else; and if, by further 
questioning, we were to get him to state why he had 
undertaken its study, we should probably find that 
he looked upon it either as a good mental gymnastic, 
or as a field in which, since no one can ever be 
right, he at least can never be wrong, whatever 
opinions he may hold. Such views are held merely 
because it is supposed, by those who entertain them, 
that philosophy is a set of ideas dissociated from all 
objects whatever, that it is, in the popular under- 
standing of the word, an 'abstract' subject. But 



134 A TEXT-BOOK OF LOGIC 

ideas which do not make some object more intelli- 
gible cannot be saved from the fate of oblivion by 
giving them a name ; and we may neglect, as falling 
below the minimum of what knowledge requires, 
this understanding of the term abstract. 

Having rejected the popular interpretation of 
the expression 'abstract idea,' we have to ask 
whether, in fact, such ideas exist, and if they do, 
under what conditions their meaning is developed. 
In answering these questions, we may remark that 
the situation with respect to abstract ideas is some- 
what as follows : If, concerning these ideas, we say 
that they are true of the objects in connection with 
which they have been formulated already in our 
experience, then they are not abstract ideas at all; 
they are, as we have seen, general ideas ; and if we 
say that they are ideas which mean nothing, we 
are talking nonsense. To illustrate, let us suppose 
that in the spring of the year, we are looking out 
upon the landscape, and that you remark, 'How 
green everything is!' Here 'green,' as you use it, 
is a general idea. If, however, in the midst of a 
conversation on monometallism, or of an unbroken 
silence, I were to say 'green,' you would naturally 
ask, 'Green what?' And if I replied, 'Green nothing, 
just green,' you would have a right to suspect my 
sanity. I can only rehabilitate myself in your re- 
gard by pointing out that 'green' is as possible an 
object of thought as 'trees' or 'grass;' and this is, 
without doubt, the course that, under such circum- 
stances, one would take. Now, in this illustration 



TERMS 135 

we have a clue to what happens when a concrete 
general idea has broken away from its moorings in 
the world of concrete fact: the meaning conveyed 
by the general idea becomes at once a new object 
of thought, which is capable of further considera- 
tion and characterisation. In brief, it is only when 
a general idea has, in this way, been dealt with as 
a subject of predication that we arrive at a true 
abstract idea. For instance, if we take our former 
illustration we may observe that although the grass, 
the oak, maple, sycamore, and elm trees, the wind- 
ing river, etc., are all 'green,' they are not the same 
greens; they vary, as the psychologist tells us, in 
tint and saturation. Now if we ask, with respect 
to this fact, what we mean by calling things admit- 
tedly different by the same name, we shall have to 
say that there is something, whether we can state 
definitely what it is or not, which is common to all 
these objects, something which we express by the 
word 'greenness.' 'Greenness' is the abstract qual- 
ity by virtue of which any object is called green, it 
is that which belongs as an attribute to all greens 
whatsoever. If, to take another illustration, we 
sort out the skeins of yarn for testing colour blind- 
ness, and ask what it is that leads us to consider 
objects which give so many different sensory im- 
pressions as belonging to a single group, we should 
doubtless, answer colour. 'Colour' (=colouredness) 
is the abstract quality by virtue of which objects 
are classified with regard to the common visual im- 
pressions that they make. Again, 'triangle' is an 



136 A TEXT-BOOK OF LOGIC 

abstract idea, because it implies the quality (tri- 
angularity) by virtue of which three-sided plane 
figures are grouped together. These illustrations 
indicate with sufficient clearness the answer that 
must be given to the question we are considering. 
Any idea which denotes certain attributes common 
to a group of concrete objects is abstract if, at the 
same time, it connotes the underlying ground of the 
similarity which exists between these attributes. 

REFERENCES 

SEE THE END OF THE NEXT CHAPTER 

QUESTIONS 

1. What is the relation of terms to propositions? 

2. What is meant by the connotative and denotative use of 
terms? Illustrate. 

3. Are terms ever used exclusively in a connotative or ex- 
clusively in a denotative sense? Explain your answer. 

4. In case a term is both connotative and denotative, are 
the connotation and denotation always equally promi- 
nent? Explain. 

5. How does any increase in the connotation of a term 
affect its denotation, and vice versa? 

6. What is the relation of the distribution of terms to the 
connotative and denotative use of terms? 

7. Explain what is meant by the distribution of terms, 
being careful to distinguish between distributed and 
undistributed terms. 

8. What is the relation of the meaning of terms to the 
connotative and denotative use of terms? 

9. What general characteristics of terms may be mentioned 
from the standpoint of connotation? 



TERMS 137 

10. Upon what do these characterictics particularly depend? 

11. How is the problem of definition distinguished? 

12. Upon what fact of our common experience does concrete 
meaning depend? 

13. In what respects does the term concrete differ from the 
word thing? 

14. What do you understand by an individual or singular 
term? 

15. Name the kinds of individual terms. 

16. Define and illustrate proper names. 

17. Are proper names used connotatively? Explain and 
illustrate your answer. 

18. Define and illustrate designations. 

19. Are designations used connotatively and denotatively? 
Explain. 

20. What is the importance of designations? 

21. Explain how meaning becomes general, and show that 
in doing so it remains concrete. 

22. What is a general, or common, term? Illustrate. 

23. Discuss the connotative and denotative use of general 
terms. 

24. Explain how meaning becomes collective, and yet re- 
mains concrete. 

25. What is a collective term? Illustrate. 

26. Discuss the connotative and denotative use of collective 
terms. 

27. What is an individual collective term? Illustrate. 

28. What is a general collective term? Illustrate. 

29. What is the relation between individual and general 
collective terms? 

30. Does this relation always hold? Explain. 

31. How does abstract, differ from concrete, meaning? 

32. Distinguish carefully between abstract and general 
terms. 

33. Discuss the connotative and denotative use of abstract 
terms. 



138 A TEXT-BOOK OF LOGIC 



EXERCISES 

1. What are the connotation and denotation of the follow- 
ing terms: 

Gentlemen my typewriter logic 

George Washington gratitude the University 

2. Show by an illustration that the denotation of a term 
may decrease if its connotation is increased. 

3. Classify in a table all the terms discussed in this chap- 
ter, showing which are coordinate and which are sub- 
ordinate. 

4. Write a list of twelve concrete individual terms, and 
indicate which are proper names, and which, if any, 
are designations. 

5. What kind of term is 'goodness' in each of the following 
statements ? 

(1) Goodness knows what we shall do. 

(2) He did it out of sheer goodness. 

6. Write a list of six general terms. 

7. Derive, if possible, abstract terms from each of those 
that occur in your answer to the previous question. 



CHAPTER V 

TERMS (CONTINUED) 

The Purpose of the Chapter. In the previous 
chapter we have traced the development of meaning 
from its concrete to its abstract form, and in doing 
so we have touched upon the main principles that 
control the logical use of terms. There are, how- 
ever, a number of other interests that lead us to 
consider objects and their qualities in ways slightly 
different from those already described, and thus to 
give our doctrine of meaning, in each case, a slightly 
different emphasis. In this chapter we shall define 
and illustrate some of these more common interests, 
and point out the varying emphasis that our mean- 
ings come to have under their guidance. 

The Basis of the Distinctions to be Studied. The 
distinctions in meaning that we are to study in this 
chapter, like those studied in the last, have a basis 
in common linguistic usage. The basis of the dis- 
tinction of concrete and abstract meaning is the 
fact that we distinguish between an object and its 
qualities, — between the object that is the possessor 
of qualities, and the qualities possessed by the ob- 
ject. The distinctions studied in the present chap- 
ter are based on this broad contrast between objects 
and their qualities, but are not identical with it. 
When, for example, we have distinguished between 
an object and its qualities, so that we can think of 
the object merely as having existence, and can think 
of qualities as possible characteristics of objects 
without at the same time identifying the objects 

(139) 



140 A TEXT-BOOK OF LOGIC 

of which they are the qualities, we can take a fur- 
ther step in regard to objects, and consider whether 
they do or do not stand in relation to other objects, 
and, in regard to qualities, whether they do or do 
not belong to certain objects. In the former case, 
we ask whether the relation that objects sustain to 
other objects affects the meaning that such objects 
have; and, in the latter, we ask whether the pos- 
session or non-possession of certain qualities by ob- 
jects in any way modifies the significance that such 
objects have for us. In the first question, we are 
concerned with what are known, in logic, as abso- 
lute and relative terms; and in the second, with 
what are known as positive and negative terms. 

Absolute and Relative Meaning. This distinction 
is one that concerns the existential character of 
objects, that is, objects considered with respect to 
whether they do or do not depend for the meaning 
they have upon the relations in which they stand to 
other objects. Stated otherwise, we are asking 
whether it is possible and useful to study objects 
independently of the connections they may have 
with other objects, and whether the terms we use 
to denote objects do or do not get part of their 
meaning from the relations which these objects sus- 
tain to other objects that fall outside the denotation 
of these terms themselves. The answer to this 
inquiry is quite obvious. Objects whose connection 
with other things is for the time being neglected 
may certainly be held before the mind as subjects 
of investigation. These objects may be quite simple, 



TERMS 141 

as a chair, or they may be quite complex, as the solar 
system. But whenever a simple or complex object 
derives its importance for consciousness from the 
fact that we ignore the connections it may have with 
other existential things, it is said to be an inde- 
pendent object. Now when the names of such objects 
are used as terms in a proposition, they are called 
absolute terms. Thus, all individual terms, whether 
they denote single individuals, or single groups of 
objects, are, in the sense explained, absolute terms. 

What we should understand by a relative term 
is more difficult to state. We shall first consider 
the most general aspect of this question. It is quite 
clear, in the first place, that since the whole prob- 
lem of meaning rests, as we have seen, upon the 
connection between the connotative and denotative 
use of terms, that there can be no object entirely 
devoid of qualities, and no quality which is not the 
quality of some object. There is always a relation 
between these two aspects of a term's meaning. 
Further, it is clear that all our meanings, whether 
concrete or abstract, singular or general, are also 
relative in the sense that the objects denoted by 
such terms stand in relation to objects denoted by 
other terms. Used in the broad way, indicated by 
these illustrations, the word 'relative' does not point 
out a particular logical distinction, but describes a 
common characteristic of all human knowledge 
whatsoever. 

The term relative is used in logic, in contrast 
to absolute, to indicate the fact that part of the 
meaning that a term has is derived from the exist- 



142 A TEXT-BOOK OF LOGIC 

ence of an object that the term itself does not denote. 
Stated another way, a relative term is one that 
implies the existence of some other object than 
the one that the term itself denotes. It is obvious 
that no concrete individual term can be relative in 
this sense. But some concrete general terms are. 
For example, the term 'father' is a concrete general 
term since it is a name which applies to an indefinite 
number of individuals in whom the relations implied 
by the name are present; it is also relative because 
these relations are such that they depend for their 
application not only upon the existence of the indi- 
vidual to whom the name is given, but also upon 
the existence of either a son or a daughter. A sim- 
ilar double relationship exists in all family connec- 
tions: uncle, grandfather, niece, etc. We may ob- 
serve the same thing in other than the family type 
of social organisation: political, — king-subject; 
economic, — debtor-creditor; juridical, — plaintiff- 
defendant; commercial, — employer-employee; do- 
mestic, — master-servant, etc. Whether this type 
of relationship is ever found outside of social organ- 
isations, or if found, whether they are common, has 
been questioned. We may point out that some logi- 
cians have been inclined to find the meaning of such 
a word as 'mountain' in the reference that it is said 
to contain to the plain from which it rises. There 
may be other words whose meanings are of this 
relative sort, such as, right-left, heavy-light, up- 
down, etc. In deciding whether any term is rela- 
tive, it should be borne in mind that the only clue 



TERMS 143 

that is of logical value, is the sense in which it is 
actually used in carefully guarded and intelligent 
speech. And by this test it appears that the words 
whose meanings are determined by the existence of 
other objects than those which such words denote 
are chiefly those that indicate the relations that we, 
as human beings, have with one another in some 
type of social organisation. 

One other point remains to be mentioned. It is 
sometimes found that when one object derives part 
of its meaning from the existence of another, the 
latter also derives part of its meaning from the 
first. Not only, for example, does uncle or aunt 
imply nephew or niece, but nephew or niece implies 
uncle or aunt. That is to say, each term of the 
relation implies, and is implied by, the other. Re- 
lationships of this kind are called reciprocal. The 
terms . between which such relationship holds are 
also called correlatives. Thus, when we regard the 
creditor-debtor relation from the standpoint of 
creditor, we say that 'debtor' is a correlative term, 
and when we regard it from the standpoint of debtor, 
we say that 'creditor' is a correlative term. By a 
correlative term, therefore, is meant that one of a 
pair of relative terms which is implied by the other. 

Positive and Negative Meaning. The distinction 
between positive and negative meaning rests upon 
the answer we give to the question whether a given 
object has or has not a certain attribute or set of 
attributes. In a general way, it is true that every 
object has or has not the attributes which the word 



144 A TEXT-BOOK OF LOGIC 

we use to point it out implies; otherwise, it may 
be asked, how can we identify any subject of dis- 
course? It may, however, be said that it is some- 
times necessary to state emphatically that the ob- 
jects we are speaking about have or have not cer- 
tain attributes, and that when this is the case, the 
meaning of what we express is either positive or 
negative. A positive meaning, to consider that first, 
calls special attention to the fact that an object has 
the attributes which are implied by the term which 
is used to point it out; and it is necessary some- 
times to emphasise this fact, because the meaning 
of what we affirm, without such emphasis, is liable 
to be misunderstood. Whenever the denotation of 
a term is unambiguous, or when its popular mean- 
ing does not render it equivocal, we do not need to 
call special attention to its precise connotation. For 
example, the term 'rent' is popularly understood as 
a fixed sum of money that is paid or received for the 
occupancy of a house or of land. It is primarily a 
denotative term, and many judgments may be ex- 
pressed which are perfectly intelligible about the 
object, — the fixed sum of money — which this term 
denotes. We may say, for example, that 'Rent is a 
constant drain upon a poor man's wages,' 'To pay 
rent all one's life is an indication of improvidence,' 
etc. In all such instances, the sense of our asser- 
tions is carried easily by the denotative use of the 
term 'rent,' However, when what we assert is 
dependent, not upon the object's existence, but upon 
its meaning, we are in a different position. In that 



TERMS 145 

case, the meaning of the term by which the object 
is denoted must be made precise if we are to have 
an intelligent understanding of what a proposition 
affirms. Thus, for the economist, the term rent is 
'the remuneration that is derived from the concrete 
things that have the value of capital,' and this mean- 
ing of the word must be kept in mind in any discus- 
sion which involves the idea for which the term 
stands. In this instance 'rent' is used connotatively, 
and, so used, it limits whatever can be said intelli- 
gently on any subject that implies the idea. It is a 
positive term because it is used to indicate the fact 
that any object to which it is applied must have the 
qualities which the term connotes. 

The Conditions of Negative Meaning. In discuss- 
ing negative meanings, we shall inquire, in the first 
place, into the conditions under which such mean- 
ings arise. We call attention to three situations 
in which knowledge is forced to assume a negative 
form. First, whenever, for any reason, we fail to 
reach a positive conclusion on any subject of inquiry, 
we may map out the progress of the inquiry by a 
series of negations. For example, let us suppose 
that a physician is called to see a patient who has 
a serious illness. As the examination of the patient 
proceeds, a number of prominent and secondary 
symptoms are noted and the possibility of typhoid, 
tuberculosis, scarlet fever, etc., suggest themselves 
in turn, only to be rejected one after the other; 
and the physician concludes his visit with a confes- 
sion, to himself if not to the family of the patient, 

10 



146 A TEXT-BOOK OF LOGIC 

that he has reached no positive knowledge of the 
disease, or complication of diseases, from which the 
patient is suffering. The physician's knowledge, in 
such a case, is made up of a series of negative judg- 
ments ; not typhoid, not scarlet fever, etc. Through 
what has been denied, that is, through what the 
physician calls his differential diagnosis, he has 
come nearer to, but has not succeded in making, a 
positive diagnosis. Negations thus mark out the 
limits within which the positive characteristics of an 
object are to be found. No doubt, in new and com- 
plicated situations, business and professional men 
are often in the position where the only thing that 
is clear to them is what not to do or think. In such 
cases, we have negative but not positive meanings ; 
but the former exist, not as something opposed to 
the latter, but as stages in our progress toward it. 
Our subject-matter refuses, one after the other, a 
number of suggested qualifications, and often we 
have to stop our investigation of the matter in 
hand before we have found the particular qualifi- 
cation which fits. 

Secondly, negative meaning arises when we safe- 
guard a positive meaning from misunderstanding 
or falsification. Let us take, as an example, the 
case where a new truth is presented for the first 
time for our understanding. We are more often in 
this relation to truth, as students, than in any other. 
The teacher, let us say, is expounding the psycho- 
logical doctrine of perception. We follow him atten- 
tively as step by step he enumerates and explains 



TERMS 147 

the various factors in the problem, and their relation 
to each other. Now the important question for us 
as students is whether we have really understood 
what the teacher has said. Class-room experience 
shows that a student's reaction to the subjects of 
his study comes most often in the form of a ques- 
tion, or a statement, which, from the teacher's stand- 
point, is the suggestion of a predicate or series of 
predicates, for the topic of discourse, — in the ex- 
ample, the psychological doctrine of perception ; and 
the teacher's problem is to determine whether the 
proposed predicates are compatible with those by 
means of which his own exposition has been carried 
on. Now, since our first apprehensions of any new 
truth are liable to be uncertain, vague, or partial, 
our proposed predicates not infrequently endanger 
our grasp of the new truth, and have to be eliminated 
from the list of those attributes which, when taken 
together, constitute the positive meaning of the sub- 
ject under consideration. Now, this elimination of 
incompatible predicates is performed by the teacher 
whenever he refuses to accept our statements or 
questions as elucidations of the subject-matter in 
hand. And his refusal is given in the form of a 
negation which means, from his point of view, that 
he is defending a positive meaning from misunder- 
standing or falsification. 

Thirdly, negative meaning arises whenever, in 
carrying forward a special line of work, our prob- 
lem is to see how far, and in what directions, our 
subject is capable of development. The starting 



148 A TEXT-BOOK OF LOGIC 

point, in a case like this, is the body of knowledge 
we have already acquired about our subject. We do 
not become possessed of the truth that lies beyond 
our grasp by a method that implies disloyalty to 
the truth that lies within it. The working criterion 
of the truth of any thing new must be the truth 
that we already possess. And this means that 
nothing becomes true which contradicts what is 
already true. Truth is a system, systematic and 
coherent, one part of which supports and supple- 
ments every other. However, this position should 
not be held in such a way that the limitations of 
the truth in hand are allowed to make us inhospit- 
able to the constantly increasing and enlarging body 
of truth. Truth, it should be borne in mind, grows 
from less to more; and, in the process, not only do 
we come into possession of new truths, but the old 
truths are transformed, and sometimes the entire 
system of truth changes its character. A familiar 
instance of this is the change from the Ptolemaic 
to the Copernican astronomy. The particular use 
of the statement and illustration in this place is to 
call attention to the fact that such changes in the 
character and system of truth is effected by nega- 
tion working within the field of established truth. 
For what is the recognition of truth's limitations 
but the admission that negation not only erects a 
barrier against outside error, but also against that 
hardening process in the heart of truth itself which, 
unchecked, steels it against the recognition of out- 
side truth? When, therefore, we are endeavouring 



TERMS 14$ 

to extend the boundaries of a particular subject, or 
when we have to consider the truth of any subject 
in its relations to other fields of knowledge with 
which it may be correlated, we are often forced into 
the position of either denying all outlying truths, 
or modifying, in the interest of the systematisation 
of truth, the knowledge that we already possess. 
Development of knowledge takes place only when 
we follow the latter course. But, we should remark, 
the modification of established truths, which is 
necessary if what is new is to find a place in the 
developing field of knowledge, is made possible by 
the elimination of what is erroneous in it ; or, stated 
otherwise, the limitations of existent truth are 
brought to light by negation working within the 
area of our established beliefs. 

The Logic of Negation. That there is such a 
thing as negative meaning is not open to serious 
question, and what the conditions are under which 
it arises we have already seen. The inquiry that 
confronts us now is, How are negative meanings to 
be interpreted? We may approach this question by 
remarking that negative meanings are developed out 
of the interests that lead us, in our inquiry into the 
nature of things, to affirmative conclusions. By 
this statement we mean that negation must be inter- 
preted as a form of knowledge, and not merely as 
an assertion of the absence of knowledge, and that, 
as such, it satisfies, in the particular instances in 
which negative meanings arise, the motives that 
sustain all our cognitive endeavours. Stated other- 



150 A TEXT-BOOK OF LOGIC 

wise, we may say that since in all knowledge thought 
is, as we have seen, in some particular relation to 
its object, we must hold either that this is true of 
negative as well as of positive meanings, or that 
negative meanings fall outside of the field of logical 
inquiry. The only alternative to this position would 
be to deny the existence of negation altogether. But 
this we cannot do. And we cannot do it for the 
simple reason that if we did succeed in getting rid 
of negation in one form, it would break out in an- 
other, — a fact that is significant of the distinctive 
function of negation in our search after the truth 
of things. An illustration of the fact just referred 
to may be found in the endeavour to get rid of neg- 
ative meanings by reducing all propositions to a 
common affirmative type. Thus, it is contended, the 
meaning of the statement, 'Some men are not Cau- 
casians,' is not, 'Some men are-not Caucasians,' 
— a negative proposition, but, 'Some men are 
not-Caucasians,' — an affirmative propostion. But, if 
this is true, it is obvious that, in the latter case, the 
predicate term has been burdened with the negative 
that belonged, in the former case, to the copula. 
And, what is more important, this way of escape 
from the difficulties of negative statements seems to 
have rendered affirmative ones equivocal. For, it 
will be remembered, in all affirmation we are sup- 
posed to predicate a positive characteristic, quality, 
attribute or relation of a subject; but when we 
affirm by means of negative terms, we seem to be 
saying that the subject does not possess the attri- 



TERMS 151 

butes connoted by the predicate of the proposi- 
tion which expresses our meaning. So far then 
from escaping the problem of negation, this attempt 
to reduce all statements to an affirmative type forces 
upon us the question of how we are to interpret 
negative terms. To this question we shall now give 
attention. 

Let us be perfectly clear what our problem is. 
When we say 'not-Caucasian,' 'not-typhoid,' etc., it 
is quite possible, as we have said, that we mean 
nothing more than that our knowledge is falling 
short of what knowledge, strictly regarded, requires. 
This, however, is a different thing from saying that 
we have attained the full measure of knowledge 
when all that we can affirm is that a subject has 
some quality or relation vaguely expressed by neg- 
ative terms. When, for example, we say of an in- 
dividual that he is not-Caucasian, or of a disease 
that it is not-typhoid, what, we should like to know, 
are the positive attributes, which these terms con- 
note? And we can ask such a question just because 
we are dealing with an affirmative statement. 
Now one way of answering this question has been 
to say that, by the exclusion of a particular group 
of attributes, expressed by the negative term, we 
include within the meaning that the negative term 
must have all other attributes whatsoever. In other 
words, the negative term, or, as it is sometimes 
called, the indefinite, indesignate, or infinite term, 
is one which divides all existing things into two 
groups, in one of which there is placed definitely 



152 A TEXT-BOOK OF LOGIC 

the excluded meaning, and in the other all other ex- 
istences and meanings. According to this view, it 
is the function of the negative term to denote the 
latter group ; it is the name of a miscellaneous num- 
ber of things, such as "accidence and adjectives and 
names of Jewish kings." Thus, as Bosanquet says, 
"not-Christian literally interpreted includes not only 
heathen humanity, but the fixed stars, the sea, and 
indeed, in Aristotle's words, 'every thing whether 
existent or non-existent' except Christian. It refers 
to no one sphere in preference to another, and thus 
says nothing definite enough to be intelligible." It 
is an example of what we may call bare negation, 
that is, of negation unlimited by any reference to a 
positive sphere of reality; and, because it includes 
so much, succeeds, in the end, in denoting nothing 
in particular. Now it may be doubted whether, out- 
side the field of a purely formal logic, there are any 
such infinite terms as this; that is, whether bare 
negation, a negation which is not a stage or step in 
our acquisition or development of positive knowl- 
edge, is ever rooted in the purposes or motives 
which, in our relation to things, give birth to rele- 
vant assertion. But if these infinite terms do not 
express meanings that are the outgrowth of the 
motives that control our knowledge processes, if, 
that is, they have no relation to the purposes that 
guide and determine the life of judgment, they lose 
all interest for logic ; they may have a psychological, 
but can have no logical, significance. 



TERMS 153 

Another way of meeting the question we are 
considering is to point out that the meaning of any 
proposition must be sought within the universe of 
discourse which the proposition implies, and that, 
consequently, this places a limitation upon the 
meaning that the proposition's terms can have. If 
from this point of view we consider the statement, 
'Some men are not-Caucasian,' it is obvious that we 
are speaking of men from the standpoint of their 
racial characteristics, and that the group of men 
which now interests us, — the 'Some men' of the 
proposition — do not have the characteristics of the 
Caucasian. But if we are making the statement at 
all intelligently, we mean more than this; we mean 
that they have the characteristics of either one or 
other of the remaining divisions of the human fam- 
ily looked at from the racial point of view. That is 
to say, the positive meaning of the negative term 
'not-Caucasian' can be expressed by 'either Negro 
or Mongolian or American Indian.' Thus, the whole 
meaning of our statement is, 'Some men are not- 
Caucasian, but are either Negro or Mongolian or 
Indian.' Likewise the other statement, 'This dis- 
ease is not-typhoid,' means that a pathological con- 
dition is present, but it is not typhoid and it is either 
scarlet fever or tuberculosis or diphtheria or one 
or other of an indefinite number of the ills to which 
the human body is subject. 

Privative Meaning. Closely connected with nega- 
tive terms are those called privative, terms which 
indicate the absence of an attribute naturally or 



154 A TEXT-BOOK OF LOGIC 

usually belonging to the object which such terms de- 
note. 'Blind/ 'maimed/ 'orphaned/ 'deaf/ are ex- 
amples. Because they are so closely connected, it 
may help us to understand both negative and priva- 
tive terms if we indicate wherein they seem to differ 
from each other. The negative term, as we have 
seen, indicates a number of positive alternatives by 
means of a negative characterisation of the object 
which such term is made to qualify. It is, there- 
fore, not a term that is negative in meaning at all ; 
it is only its form that has this characteristic. The 
reverse seems to be true of privative terms, their 
meaning is negative, and what is negated is defi- 
nitely the attribute or attributes which such terms 
connote. Thus, 'The boy is an orphan/ must be 
understood to mean that he has no parents, — 'the 
absence of parents' being what the term 'orphan' 
connotes. A further difference between these terms 
may be indicated. In the case of negative terms, 
we are able, through what is denied, to affirm cer- 
tain alternative qualities, that is, to go beyond what 
is definitely stated by such terms. In the case of 
privative terms, this is not true. Of the boy who is 
an orphan, all that we can positively affirm is that 
he has no parents; we cannot say whether he has 
either a brother, or sister, or uncle or aunt. If of 
any one we can say, 'He is deaf/ we do not find in 
this statement any ground of assertion with respect 
to the presence, absence, or degree of acuteness of 
any of his other faculties. In view of these charac- 
teristics, privation must be interpreted as an ex- 



TERMS 155 

treme case of negation ; that is, of a negation which 
arises under conditions that make defect of quality 
a differentia of the meaning we intend to convey. 

Disparate and Contrary Meaning. We may touch 
upon two other related distinctions which have neg- 
ative significance. Whenever we can divide a class 
of objects into a number of mutually exclusive 
classes, as, for example, the class animal into lions, 
tigers, etc., these subordinate classes are said to be 
disparate. If, further, we can arrange the exclusive 
classes of a group of objects with respect to their 
possessing more or less of some quality, for ex- 
ample, organisms in a series from amoeba to man, 
and if we can say of two of these classes that, with 
respect to the common quality, they differ from 
each other in a greater degree than either does 
from any other, the relationship between these two 
most differing classes is said in logic to be that of 
contrariety. A contrary relation is one form of 
negative meaning, and indicates the greatest degree 
of exclusion, actual or possible, within a single 
genus. In other words, contraries are the extreme 
limits of the universe of discourse within which the 
meaning of any proposition falls. 

REFERENCES 

H. A. Aikins, The Principles of Logic, Ch. V. 

B. Bosanquet, The Essentials of Logic, Lect. V, 4-7. 

J. E. Creighton, An Elementary Logic, 3d Edition, Part I., 
Ch. IV. 

W. S. Jevons, Elementary Lessons in Logic, Chs. III-V. 

S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
tion, Ch. II. 



156 A TEXT-BOOK OF LOGIC 

W. Minto, Logic, Inductive and Deductive, Part I., Ch. I. 

C. Read, Logic, Deductive and Inductive, 3d Edition, Chs. III., 

IV. 
W. J. Taylor, Elementary Logic, Ch. II-IV. 

ADVANCED 

J. M. Baldwin, Thought and Things, Vol. II., Part II., Ch. 

VII. 
B. Bosanquet, Logic, Vol. I., pp. 46-71. 
F. H. Bradley, The Principles of Logic, pp. 155-173. 
W. R. B. Gibson, The Problem of Logic, Chs. I., VII., VIII. 
H. W. B. Joseph, An Introduction to Logic, Chs. II., VI. 
J. N. Keynes, Studies and Exercises in Formal Logic, 4th 

Edition, Part I., Chs. I., II. 
H. Lotze, Logic, Vol. I., Ch. I. 
J. S. Mill, A System of Logic, Book I., Ch. II. 
J. Venn, Empirical Logic, Ch. VII. 
J. Welton, A Manual of Logic, Book I., Chs. I., II. 

QUESTIONS. 

1. How are the logical distinctions of absolute and rela- 
tive, positive and negative terms, related to those dis- 
cussed in the previous chapter? 

2. Upon the answer to what question does the distinction 
of absolute and relative depend? 

3. State and illustrate the meaning that belongs to abso- 
lute terms. 

4. What senses of the term relative are excluded from our 
discussion of relative terms? 

5. What is meant in logic by a relative term? 

6. What class of experience provides most of our illustra- 
tions of relative terms? 

7. What are correlative terms? 

8. Upon the answer to what question does the distinction 
of positive and negative depend? 

9. What is a positive term? 

10. Under what conditions do we express our meaning pos- 
itively? 



TERMS 157 

11. State and explain the conditions under which our knowl- 
edge has to be expressed negatively. 

12. Are the motives that lead to negative statements differ- 
ent from those that lead to affirmative ones? Explain. 

13. How have some logicians tried to get rid of negative 
meaning? 

14. Criticise this effort. 

15. State and illustrate two views of the logical significance 
of negative terms. 

16. What do you understand by privative meaning? 

17. How are privative related to negative terms? 

18. What do you understand by disparate and contrary 
meaning? 

EXERCISES 

1. Write three propositions to illustrate the absolute mean- 
ing of terms. 

2. Discuss each absolute term in your answer to the pre- 
vious question to show whether it is concrete or abstract. 
Write new propositions to illustrate your results. 

3. Write new propositions to illustrate concrete and ab- 
stract terms. 

4. Write three propositions to illustrate the relative mean- 
ing of terms. 

5. Discuss each relative term in your answer to the pre- 
vious question to show whether it is concrete, abstract, 
absolute. Illustrate. 

6. Write three propositions to illustrate the positive mean- 
ing of terms. 

7. Discuss each positive term in your answer to the pre- 
vious question to show whether it is concrete, abstract, 
absolute, relative. Illustrate. 

8. Write three propositions to illustrate the negative mean- 
ing of terms. 

9. Discuss each negative term in your answer to the pre- 
vious question to show whether it is concrete, abstract, 
absolute, relative, positive. Illustrate. 



CHAPTER VI 
DEFINITION AND THE PREDICABLES 

The Questions of this Chapter. In our study of 
terms, in the two preceding chapters, we saw first, 
that a term may be used either to point out par- 
ticular existing things or to convey some meaning. 
When a term is employed to point out particular 
existing things it is said to be used denotatively; 
when it is employed to convey some meaning, it is 
said to be used connotatively. Arising out of this 
distinction of the denotative and connotative use of 
terms, certain problems were forced upon us for 
consideration. For instance, our study of the deno- 
tative use of terms brought before us the problem 
of the distribution of terms, and our study of the 
connotative use of terms brought to our attention 
certain general characteristics of terms the study 
of which, as we may now say, involved the problem 
of the classification of terms. In our statement of 
this latter problem, we were led to recognize another 
problem, — the ^problem of definition, — and this 
problem was said to be concerned with the way in 
which the particular meaning of terms receives 
logical formulation. The facts and relations em- 
bodied in this statement of the logic of terms may 
be expressed in a tabular form as follows : 

(158) 



DEFINITION AND THE PREDICABLES 159 

Standpoint Problem 

C Denotation Distribution of terms 



Terms 



Connotation 



f Classification of terms 
I Definition of terms 



This table may be read as follows: Terms studied 
from the standpoint of their denotation give rise 
to the problem of the distribution of terms ; studied 
from the standpoint of their connotation, they give 
rise either to the problem of the classification of 
terms or to the problem of the definition of terms. 

Of the two problems connected with the conno- 
tative use of terms, the problem of the classification 
and of the definition of terms, the former may be 
said to be concerned with the question, What are 
the various kinds of terms that form the S and P 
of logical propositions ? And the latter is concerned 
with the question, What, irrespective of the kinds 
that terms may be, are the meanings that terms may 
have? We have considered the first of these ques- 
tions in the two previous chapters. The second 
question we shall study in the first part of the pres- 
ent chapter. In this part, we shall try to show how 
to make the particular meanings of the terms we 
employ definite, how to formulate them in such a 
way that no doubt remains as to the sense in which 
they are used. We hope, as the result of our study, 
to learn how to proceed when we are required to 
make the meaning of any of our terms explicit, 



160 A TEXT-BOOK OF LOGIC 

After we have concluded this study, we shall be in 
a position to ask and answer the question, What 
kinds of things can be predicated of a subject? 
The convenience of discussing this question here 
is that doubt has been cast upon the possibility of 
predicating of any subject its own definition. But 
it is more than a question of convenience; for, as 
we shall see, our whole view of the nature of defini- 
tion is involved in the position we take with respect 
to the predicables. There are, then, two problems 
to be discussed in this chapter, the problem of defi- 
nition and the problem of the predicables, and of 
these the first to be considered is the problem of 
definition. 

Non-Ambiguity. We may approach the study of 
this question by calling attention to the fact that in 
the fields of science, more than anywhere else, our 
ideas must be accurate, and the language in which 
these ideas are expressed must definitely convey the 
meaning intended. That is to say, the natural fluid- 
ity of language must not be allowed to go in the 
sciences to the point of ambiguity. Whenever, 
that is, we wish to express our ideas in words, there 
is a limit to the indefiniteness that can be allowed 
to the forms of our speech, and if we really convey 
the sense of what we mean our words must be 
definite in what they connote. 

This demand for precision in the use of words 
may be easily misunderstood, and it may lead to an 
effort after the impossible or undesirable. The aver- 
age man's impatience with over-primness of speech 



DEFINITION AND THE PREDICABLES 161 

is a healthy protest against pedantry ; but the same 
man's laxness in the use of words bears witness 
quite often to the vagueness of his ideas. These are 
the extremes against which it is desirable to guard : 
the extreme, on the one hand, of an accuracy of 
speech out of all proportion to the character and 
importance of the subject-matter of our thought; 
and the extreme, on the other hand, of being tyran- 
nised over by words and of using them as substi- 
tutes for ideas. There is always an appropriate 
exactness that we should strive to realise in our use 
of language, and nothing more than this can be 
demanded of us by the strictest logic. We must aim 
to make our speech non-ambiguous, but non-ambi- 
guity is relative to the purpose of the speaker and 
to the subject of his thought. Non-ambiguity 
changes with the change of purpose and subject, 
and the degree of exactness that is requisite on 
some occasions and with respect to some subjects 
might be altogether inadequate if these were differ- 
ent. There is no one standard of explicitness that 
we are required to attain ; the most that can be de- 
manded is that on all occasions, and with respect 
to all subjects, our language be made a fitting ve- 
hicle for the expression of the ideas we wish to 
convey. 

We have called attention to these somewhat 
obviaus considerations, because, through their neg- 
lect, the importance of the problems with which we 
are here concerned has frequently been obscured. 
11 



162 A TEXT-BOOK OF LOGIC 

This, we think, is unfortunate; for whatever can 
help us to avoid misunderstanding, whatever can 
strengthen our reputation for saying what we mean 
and meaning what we say, cannot be of indifference 
to any one of us, in a world where intellectual integ- 
rity is coming to play an increasingly important 
part. 

These considerations may also enable us to see 
that whenever we are in danger of being misunder- 
stood, whether in science or literature or business, 
on account of the indefinite meanings of the words 
we employ, there is required some method by which 
the misunderstanding can be avoided, some method 
by which words can be moulded to the uses of ideas. 
Life is one, and the occasions when it is necessary 
to state explicitly the meaning of the words we use 
arise all along its way, and are not confined to, even 
if they are more frequent and more urgent in, the 
various departments into which our human knowl- 
edge has been organised. In other words, ambiguity 
may be as undesirable in the drawing-room or 
counting-house as in the laboratory, and whenever 
and wherever it is a hindrance, we naturally try 
to get rid of it. But before we consider how this 
may be done, a word may be added on ambiguity 
itself. 

Ambiguity. The traditional doctrine of ambi- 
guity may be briefly stated. Any term is ambig- 
uous if it is given a meaning in a proposition which 
it does not have in the judgment which the prop- 
osition expresses. For example, 'He was a man who 



DEFINITION AND THE PREDICABLES 163 

always chose a mean line of action.' Terms that 
have more than one meaning, and which, therefore, 
lead to ambiguity of statement, are called ambig- 
uous or equivocal; and, in contrast to these, those 
that have only one meaning are called unambig- 
uous or univocal. 

There are two respects in which this view of 
ambiguity does not seem to be satisfactory. First, 
it implies too formal or mechanical a view of logic. 
It leaves the impression that words are like counters 
in a game to be pushed here and there as the exi- 
gencies of the game demand, that no difference is 
made to the words themselves by their change of 
relation in different propositions. Second, it sup- 
poses that there are certain words which have a 
fixed meaning, and that the statements in which 
they occur are, therefore, free from ambiguity. 
This is difficult to maintain for any class of words, 
and if it were true of particular words there is no 
guarantee that it must remain so. The principle 
that should guide us in a discussion like this is that 
it is not words that make a language, but language 
that moulds words and fits them to the uses for 
which the language exists. For example, the word 
'Democrat' has a definite historical meaning, as also 
has the word 'Republican' ; but as names of political 
parties they no longer mean what they meant origin- 
ally, and have become vague and indefinite through 
the growth within each party of sub-classes or 
varieties of democracy and republicanism, each of 
which would deny to the other the right to the name. 



164 A TEXT-BOOK OF LOGIC 

This process of splitting off from a perfectly clear 
centre of meaning is going on all the time in the 
living languages of the world, and is giving rise to 
conflicting meanings in the uses of words. 

The problem of ambiguity may be viewed in a 
broader way still. Instead of considering it as hav- 
ing to do with the indefiniteness that arises from the 
vague or shifting meaning of words, we may view 
it as in some sort the central or fundamental prob- 
lem of the science of logic itself. For logic, as we 
have seen, is a study of the methods by which mean- 
ings can get asserted, and how asserted meanings 
can get expressed in propositions. It is because 
meaning tends to elude us, and because words are 
not always, if they are ever, faithful representatives 
of ideas, because, that is to say, ideas and words 
are both equivocal, that we are compelled, if the 
aims of thinking are to be attained, to study the 
sources of this uncertainty, and to derive guidance 
from the knowledge that we thus obtain. Ambi- 
guity, therefore, is a term that describes a natural 
condition of human thinking, as well as a natural 
indefiniteness of human speech. But, as we all 
know, vagueness in an idea and indefiniteness in 
speech, have many sources ; and it will not be until 
we have reached the end of our studies that we 
shall have reviewed even the more important ones. 
Ambiguity in the meaning and application of words, 
therefore, is part of a much larger problem ; but in 
this chapter we shall consider only the ambiguity 
that arises in connection with our use of words. 



DEFINITION AND THE PREDICABLES 165 

Translation. One of the most common means for 
the removal of ambiguity is translation. Thus, if 
what we say is not understood, or is in danger of 
being misunderstood, we often translate the same 
idea into another set of words in the hope that the 
ambiguity may be removed. This is a common prac- 
tice both in literature and in ordinary conversation. 
When, for example, Shakespeare makes Hamlet say, 

O, that this too too solid flesh would melt, 
Thaw, and resolve itself into a dew; 
Or that the Everlasting had not fixed 
His canon 'gainst self-slaughter! 

he is putting into Hamlet's mouth words that ex- 
press a single idea twice over, namely, the longing 
for death as a means of escape from his troubles. 
If, again, a teacher should ask his class a question 
which fails to elicit the correct answer, he would 
probably restate the question in the light of the 
difficulties that the answers had thrown upon the 
class's understanding of the question as first stated. 
If further, to take an illustration already used, we 
were to say of a given individual, 'He was a man 
who always chose a mean line action/ and we were 
misunderstood to say that he was a man 'devoid of 
a generous disposition', we should probably substi- 
tute for the word 'mean/ the word 'moderate' in a 
re-statement of what we had intended, in the first 
place, to say. There is no doubt that this habit of 
translating into a variety of forms the ideas we wish 
to express is so inveterate that most of us talk more 



166 A TEXT-BOOK OF LOGIC 

than is necessary for understanding, and many of 
the books we ordinarily read are much longer than 
they need be. But the care we exercise in making 
our meaning clear is grounded in a healthy instinct ; 
it is the respect we pay to the demand for unambig- 
uous statements. 

When Translation may be Employed. If we look 
at the class of cases illustrated in the preceding 
paragraph, we shall discover that the source of their 
ambiguity does not lie in the fact that our words 
have a vague fringe of meaning, but that the centre 
or core of meaning has been misunderstood. When- 
ever ambiguity arises from our unfamiliarity with 
the meaning of the words in which ideas are ex- 
pressed, what is needed is that the same idea be 
translated into a set of words with the meaning of 
which we are familiar. 

In translation, then, ambiguity arises from the 
fact that the central meaning of a word is not pre- 
cisely determined, either because the word carries 
no meaning at all, or because it carries a meaning 
that renders the whole sentence indefinite. If, for 
example, you do not know what the word 'com- 
mandeer' means, you are not likely to understand 
any statement in which the word occurs, for 
example, 'My motor has been commandeered.' To 
meet such a situation it is obvious that some other 
word or explanatory statement would have to be sub- 
stituted for the meaningless 'commandeered.' If, 
to take another case, a class in logic were given the 
task of stating the meaning of the assertion 'Non 



DEFINITION AND THE PREDICABLES 167 

omnis moriar (I shall not all die),' and it proved 
difficult or impossible, the reason would be that am- 
biguity spreads over the whole sentence from the 
indefiniteness of the word 'all,' an indefiniteness 
that is not due, as in the former illustration, to the 
absence of meaning, but to the conflict of two mean- 
ings that are not clearly distinguished. In this ex- 
ample, the Latin word omnis has a distributed mean- 
ing, and if the Roman had wished to express the 
collective meaning of 'all,' he would have written 
cunctis. We have only, therefore, to point out the 
distributed use of the word 'all' to enable the student 
to see that the meaning of the statement is 'some 
part of me is immortal.' 

When Definition is Required. The conditions un- 
der which definition is required are different from 
those under which translation is most effective. 
Definition is called for when the work-a-day mean- 
ing of the word that requires defining is already 
known, but is becoming obscured by the fact that, 
through the similarity of its meaning to other 
words, its distinctive characteristics are in danger 
of being overlooked. For instance, the most obvious 
common characteristic of the violin, viola, 'cello, 
and bass viol is their shape, and it is this that 
leads one to regard all of them, on first ac- 
quaintance, as, let us say, violins. Our knowledge, 
that is to say, emphasises the common likeness that 
exists between the several instruments named, and 
there is confusion of one thing with another because 
the differences which give to these objects a distinct 
place in the universe of musical instruments have 



168 A TEXT-BOOK OF LOGIC 

been overlooked. The confusion does not arise from 
what is included, but from what is omitted, and 
what is omitted, in this case, lies, outside the centre, 
at the boundaries of the words' meanings. To state 
it generally, the meanings of closely related words 
encroach upon one another when the boundaries 
that keep their meanings distinct are overlooked or 
broken down. Now it often happens that the sense 
of what we say depends to a large extent upon a 
word's ability to suggest just such differences 2 , 
in the illustration used, we persistently ignored. 
When this happens ambiguity is sure to result, an 
ambiguity, let it be observed, that is due to the con- 
fusion of closely related things. In such a case, the 
practically important problem is to find some 
method by which ambiguity of the kind here in 
question can be overcome when it exists, or be 
avoided when it does not. 

The Method of Definition. In any case of ambi- 
guity that can be overcome by definition, the indefi- 
niteness of the word's meaning which occasions the 
ambiguity is due to our failure to mark off the 
boundaries of this meaning from those of other re- 
lated meanings. Indefiniteness of this sort in the 
meanings of words may be illustrated if we ask our- 
selves, for example, what we understand by a bal- 
loon and an air-ship. The conspicuous central mean- 
ing of the two words is doubtless the fact that they 
are machines that travel in the air ; but if they mean 
no more than this, we shall very soon be calling eac,b 
by the name of the other, or we shall be calling ctii 



DEFINITION AND THE PREDICABLES 169 

machines that travel in the air by the name of the 
one or the other. It is in cases like this, as we have 
seen, that the definition of words is necessary. 
How, then, shall we go about the task of defining? 
Obviously, by the way of comparison, by the com- 
parison of the things which our words denote. Thus, 
if we wish to make our meanings of the words bal- 
loon and air-ship precise, we compare an air-ship 
with a balloon, and this comparison will lead to the 
discovery that they differ from one another in the 
method of their locomotion: the air-ship is driven 
by an engine and the balloon is not. We shall, then, 
call anything an air-ship which travels in the air 
and is driven by an engine, and the word balloon 
will be reserved for any air-traveling machine which 
depends for its locomotion upon the air-currents. 
This method of definition is for all ordinary purposes 
the most practical, and it lends itself to the require- 
ments of the specific occasions which make defini- 
tion imperative. We get, that is to say, the mean- 
ing that suits the purpose of the statement. Con- 
stant practice in the comparison of what words 
denote will not only render our meanings more pre- 
cise, but free us from that indefiniteness which 
comes from an exclusive familiarity with the dic- 
tionary meanings of words; for what a dictionary 
cannot do, and what comparison does, is to render 
the meanings of words appropriate to the particular 
contexts in which they occur. By the method of 
comparison we find the relevant meaning, the mean- 
ing that is required by the universe of discourse 



170 A TEXT-BOOK OF LOGIC 

within which our thought is moving, and by the 
purpose which controls our particular assertions. 

Definition per genus et differentiam. By defini- 
tion, as we have seen, we aim to substitute definite- 
ness for indefiniteness in the meaning of our words, 
and thus to avoid ambiguities of statement. We 
have seen, also, that not all cases of ambiguity are 
overcome best by definition, but only, or particularly, 
those cases in which the vagueness of the boundaries 
of a word's meaning obscures the sense of what 
we wish to say. In definition, therefore, we seek 
to limit the range of a word's meaning, by giving 
an appropriate degree of definiteness to its fringe 
or outlying area. 

Now it is quite obvious that we cannot limit 
the meaning of our words in the way required by 
definition if these words are used or understood by 
us with no meaning at all. We cannot talk about 
limiting the extent of our words' meanings unless 
these words are used, and are understood, in some, 
however vague, sense. Hence, as we said above, 
the central meaning of words is not in question in 
these cases of ambiguity ; it is only the range of the 
word's meaning that is in doubt. It would seem, 
therefore, that the limitations that we put upon 
our meanings in defining them must have some rela- 
tion to these meanings themselves, but the particular 
direction in which the limitation is made depends 
upon the purpose for which we are seeking the defi- 
nition. To take a simpler illustration, if the purpose 
for which we need a definition of 'water' is domes- 



DEFINITION AND THE PREDICABLES 171 

tic, we may say that it is a liquid which is useful 
for cleansing; but if our interests are chemical, we 
must say that the liquid is composed of two mole- 
cules of hydrogen and one of oxygen. In both in- 
stances, we start with the central idea of water as 
a liquid, and in both we limit the range of this 
meaning in a direction which is determined by the 
purpose or interest that the definition is to serve. 
It would seem, consequently, that every definition 
has two parts, a central and a peripheral, and that 
these are different, though related, aspects of a 
word's explicit meaning. 

Now the two parts of which, as we have seen, 
the meaning of words is comprised are called in 
logic the genus and the differentia respectively. By 
the genus we mean the clear centre, and by the 
differentia the vague periphery of a word's conno- 
tation. The connection between the two is obvious 
if we remember that both are specifications of a 
single meaning. Since, therefore, in denning a 
word's meaning we start with the recognition of 
its genus, the differentia cannot add to that meaning 
anything inconsistent with what the genus already 
connotes. That is to say, we must look within the 
range of meaning broadly marked out already by 
its genus for the marks that make the meaning of 
a word distinct. The differentia must lie within the 
genus, and not outside it, if we are to mark off from 
encroaching meanings the one that, by definition, 
we are trying to make distinct. For what lies out- 
side any genus belongs to another genus, or is that 



172 A TEXT-BOOK OF LOGIC 

genus itself, and is not likely to threaten us with 
ambiguity; but the distinctions that lie within a 
genus are likely to be overlooked because of the com- 
mon meaning that pervades all that belongs to the 
genus. For example, no one is in any danger of 
confusing a typewriter with the table on which it 
stands because each belongs, in our common ac- 
quaintance with it, to a different genus, the one to 
the genus 'objects for writing with,' and the other to 
the genus 'objects for placing things upon/ But if, 
to take another illustration, the poet or philosopher 
or scientist were to mistake the world of his imagi- 
nation for the world of his actual experience, this 
would be because he had failed to observe the marks 
that keep the two worlds distinct. If, again, the 
student were to use the words 'university' and 'col- 
lege' synonymously, this would be because he had 
failed to notice, within the meaning that both have 
in common, the specific difference by which the one 
is distinguished from the other in the same genus. 
From these statements and illustrations it is obvious 
not only how genus and differentia are related to 
each other in a logical definition, but also what the 
terms themselves signify. Thus, by a genus is meant 
a group of qualities belonging to a number of par- 
ticular objects in common. The word is also used to 
denote any group of objects when these objects are 
thought of as possessing common qualities. By a 
differentia, on the other hand, is meant the specific 
difference by which a distinct place is given to an 
object within a genus by reason of its possessing a 



DEFINITION AND THE PREDICABLES 173 

quality, or group of qualities, that does not belong 
to any other member of its genus. Hence, in looking 
for the differentia of an object we must look for some 
quality, or group of qualities, that does not belong to 
any other object of the group to which this object 
belongs. When this quality or group of qualities 
is not clearly apprehended we are liable to confuse 
one thing with another. 

Verbal and Real Definition. The distinction be- 
tween real and verbal definition, or, as it is some- 
times stated, between scientific and nominal defini- 
tion, is as old as Aristotle, although in the case of 
verbal definition modern writers do not seem agreed 
as to how it should be understood. By a real or 
scientific definition is meant a definition that is based 
upon and gives a description of the essential nature 
of the object which the word to be defined denotes. 
Far example, a 'liquid' is defined as that form of 
matter in which the molecules move with perfect 
freedom without changing their size. Verbal or 
nominal definitions, on the other hand, have received 
at least two different interpretations. The first, or 
Aristotelian, interpretation bids us regard as ver- 
bal definitions the current or popular meanings of 
words. For example, the definition of a house as 'a 
building in which people live' would be, on this in- 
terpretation, a verbal definition. The second inter- 
pretation would make any definition verbal when 
the word in question is used to indicate what any- 
thing is called. For example, the definition of the 
word 'dog' is verbal when it fails to convey any 



174 A TEXT-BOOK OF LOGIC 

information about the essential qualities of the ob- 
ject that the word denotes, and connotes only those 
qualities which make the use of the word appro- 
priate. 

Now the distinction of real and verbal definition, 
and the variations of the sense in which verbal defi- 
nitions are understood, are interesting, from a log- 
ical point of view, because they raise the question 
whether in definition we are dealing with thoughts 
or things, with the nature of objects, or with our 
interests and purposes in their relation to objects. 
According to the view of logic which we are ex- 
pounding, no answer can be given to this question 
which ignores the intimate connection of thoughts 
and things. In the pursuit of knowledge, we are not 
interested exclusively in either thoughts or things; 
knowledge, as we have shown, exists in the form 
of though ts-about-things. If this is borne in mind, 
it will be evident that in all our efforts to avoid 
ambiguity we strive to bring our thoughts into rela- 
tion with things, and things into relation with 
thoughts; and in definition it is sometimes the one 
and sometimes the other of these factors of knowl- 
edge that requires to be made explicit. In the light 
of this statement, the distinction of verbal and real 
definition is not an absolute but a relative one, and 
were it not for the fact that our words need to be 
wedded to fixed meanings, and meanings to be fixed 
and made definite by the use of words, the distinc- 
tion would have no particular logical interest, and 
might vanish entirely. The distinction, however, 



DEFINITION AND THE PREDICABLES 175 

persists and is likely to persist, because our knowl- 
edge is always in different stages of development, 
and because with the improvement of knowledge 
old words receive more precise meanings, and new 
terms are constantly taking their place in the vocab- 
ulary of the people. But while this is true, it is 
quite clear that the goal toward which we move in 
definition is a truer insight into reality, and the 
preservation of this insight in terms that adequately 
express it. 

The Relation of Purpose to Definition. We have 
said that the aim of every definition is to make our 
knowledge of things more precise, and to fix this 
knowledge in words. So far as this is true, we are 
emphasising the relation of definition to the objects 
of our knowledge. But what objects and what fea- 
tures of objects are of importance for knowledge, 
depends upon the purpose for which the definition 
of these objects is sought. A change in purpose is 
liable to produce a corresponding change in the defi- 
nition. For example, if my purpose is to ascertain 
the structural character of a circle, my definition 
will call attention to the fact that a circle is a plane 
figure bounded in such a way that all straight lines 
drawn from a fixed point, called the centre, to this 
bounding line are of equal length. If, on the other 
hand, my purpose is to enable one to draw a circle, 
it will then be defined as the plane figure described 
by a point moving at a given distance around an- 
other fixed point. This is called, in contrast to the 
structural, a genetic definition. It should be ob- 



176 A TEXT-BOOK OF LOGIC 

served that the distinction between structural and 
genetic definition is not confined to mathematics; 
the distinction, that is, does not depend on the sub- 
ject matter, but upon the purpose for which the 
definition is sought. But every case of definition 
whether structural or genetic is per genus et differ- 
entiam, a form of definition which we must take as 
typical of all definition whatsoever. 

Tests of a Definition. In text-books of logic, it 
is customary to enumerate a number of other rules 
of definition than the one to which our attention has 
been exclusively directed. There results from this 
mode of presenting the subject an impression of 
complexity and difficulty that is really foreign to it, 
and the student is deprived of the incentive that 
comes from a simple and unencumbered statement 
to make a practical use of that rule. We, therefore, 
emphasise again the fact that all definition is to be 
sought per genus et differentiam, and that this rule, 
when properly applied, relieves of ambiguity any 
statement that is caused by indefiniteness in the 
meaning of words, and that it is the only one where- 
by this result can be accomplished. 

The only question remaining on our hands is, 
then, how we are to know whether the rule has been 
properly applied. It is as an answer to this ques- 
tion that the other so-called rules have their value; 
and because they provide us with an answer to this 
question they are not rules of definition at all, but 
tests of the accuracy of definitions reached in some 
other way. We shall consider them in this light in 



DEFINITION AND THE PREDICABLES 177 

the following paragraphs, and thereby make the 
one rule of definition itself more definite. 

In the first place, let us recall the fact that the 
object of definition is to limit the extent of a word's 
meaning, and in limiting it to make it more exact. 
Omnis determinatio limitatio est: we make our 
knowledge of objects definite by limiting the range 
of the object's nature of which our knowledge, at 
any time, takes account. Nowhere more than in the 
intellectual life does the proverb 'grasp all lose all' 
have a more pertinent application. Only if we are 
willing to let some things go, can we gain anything 
at all. But in order to gain something, we must 
systematically eliminate what does not have a bear- 
ing upon the purpose for which knowledge is being 
sought. And, as we have shown, definition is a 
means of systematically eliminating encroaching 
meanings which are threatening the definiteness of 
our assertions. It would seem, therefore, that one 
of the dangers to which our definitions may be ex- 
posed is to be found in their particular range : our 
definitions may be either too broad or too narrow. 
We shall examine each of these cases separately. 

If the genus of a definition is not proximate our 
definition is likely to be too broad. For example, if 
we define a square as a quadrilateral figure {genus) 
whose angles are right-angles (differentia), it is 
obvious that we are in danger of confusing a square 
with an oblong which is also a quadrilateral rec- 
tangular figure. The definition is too wide. To 

12 



178 A TEXT-BOOK OF LOGIC 

rectify the definition we shall have to compare the 
square with an oblong, and then we shall observe 
that while both are quadrilateral, this is not their 
nearest genus, that is, it does not contain all the 
qualities that they have in common. Besides being 
quadrilateral they are both rectangular. The class, 
therefore, to which they both belong is quadrilateral 
rectangle. Now, within this class, the differentia 
of the square will be equilateral, having all its sides 
equal. Our finished definition of a square will, 
therefore, be 'a quadrilateral rectangle having all its 
sides equal/ 

If the differentia of a definition is not exact our 
definition is likely to be too narrow. By the differ- 
entia being exact we mean that it must be such that 
only the objects denoted by the term we are defining 
possess the attribute in question. Suppose we were 
to define man as a civilised animal, the differentia 
'civilised' would not be exact, and the definition too 
narrow, because it excluded from the class, man, 
all individuals who had not reached a certain stage 
of culture. To test the accuracy of our differentia 
we may ask ourselves the question : Do all and only 
the objects denoted by the term we are defining 
possess the quality connoted by the differentia by 
means of which we are seeking to mark off the 
meaning of the term from that of other closely 
related terms? If not, the definition will be too 
narrow. 

After we have done the best we can to secure 
the accuracy of our definition in the ways mentioned. 



DEFINITION AND THE PREDICABLES 179 

we may then examine the definition as a whole. We 
can do this if we remember that a true definition 
can always be simply converted. If it is true, for 
example, that 'a house-dog is a domestic animal that 
barks,' then, if our definition is accurate, it must be 
true that 'a domestic animal that barks is a house- 
dog.' That is to say, the object defined (the defini- 
endum) and the definition must be commensurate. 
Or, to state the same fact another way, whatever 
can be relevantly predicated of the object defined 
must be predicable of the definition, and vice-versa. 
This rule guards against anything superfluous in 
definition. 

Further, the terms of the definition must be of 
the same order as the term defined. If, for example, 
we defined the body as 'the visible garment of the 
soul,' it is obvious that the word soul belongs to the 
order of spiritual facts, and is transferred to the 
physical order, the order of the term defined. The 
uselessness of definitions of this kind may be over- 
come if we take our clue to the order of the terms 
in which our definition must be stated from the 
order of the term to be defined. Hence, to satisfy 
this requirement, we may ask ourselves the ques- 
tion: Are all the terms of the definition homo- 
geneous with the term defined? In this way we 
avoid the indefiniteness that arises from the use of 
figurative language. 

Another requirement of a good definition is that 
the terms of the definition should be more ele- 
mentary than the term defined. The elementariness 



180 A TEXT-BOOK OF LOGIC 

of a term is determined with reference to the uni- 
verse within which the term to be defined belongs. 
For example, the terms 'rational' and 'animal' are 
more elementary than the term 'man' of which they 
are predicated as the definition; and in the same 
way the terms 'mammal' and 'living in the ocean' 
are more elementary than the term 'whale.' By ele- 
mentary, that is, is meant elementary in the field 
of knowledge to which the term to be defined re- 
fers, and not to the range of information that may 
at any time be current. Hence, for one who has no 
acquaintance with the field of knowledge with which 
the term is connected, we may remove the ambi- 
guity that exists in the meaning of the term better 
by pointing out a specimen of the class or kind of 
thing that the term denotes than we can by a 
definition. 

Again, a term must not be defined by the use 
of the term itself or by one of its synonyms. If 
this occurs we have what is called a circular defini- 
tion. For example, if we define a power as 'a force 
that tends to produce motion,' we are obviously 
guilty of a breach of this requirement since the word 
force has the same meaning as the word to be de- 
fined. 

Finally, the form of our definition must be pos- 
itive if the term to be defined is positive, and neg- 
ative if the term to be defined is negative. For 
example, the term 'gentleman' has a positive mean- 
ing, and, therefore, it would be a breach of this 
requirement if we were to define it as 'a man who 



DEFINITION AND THE PREDICABLES 181 

has no definite means of support.' But if we were 
to define an alien as 'a man who is not a citizen of 
the country with respect to which he is declared an 
alien/ we should satisfy the requirement, because 
the term alien carries with it a negative meaning. 
The Problem and Classification of the Predicables. 
Whatever can be predicated of a subject is called 
a predicable. Now if we ask ourselves the ques- 
tion, What sort of things can be predicables, i. e., 
can be predicated of a subject? we have definitely 
placed before ourselves an inquiry that engaged the 
attention of Aristotle, and again of Porphyry six 
hundred years after Aristotle's time. The answers 
that Aristotle and Porphyry gave to this question 
may be placed in two separate columns thus : 

ARISTOTLE'S LIST OF PORPHYRY'S LIST OF 

PREDICABLES PREDICABLES 

Definition Genus 

Genus Species 

Differentia Differentia 

Proprium Proprium 

Accident Accident 

The various kinds of things that can form the pred- 
icates of logical propositions are the kinds of things 
indicated by the names in these two lists. 

An examination of these lists will show that they 
differ in the substitution by Porphyry of 'species' 
for Aristotle's 'definition,' the other four predi- 
cables being the same. But although apparently 
only a slight difference, this change indicates a dif- 



182 A TEXT-BOOK OF LOGIC 

f erence in the doctrine of definition of sufficient sig- 
nificance to demand a word or two of explanation. 
The significance of this difference in the two lists 
can, perhaps, be seen if we remark that the question, 
What sorts of thing can be predicated? is not un- 
connected with the question, What kinds of thing 
can be defined? We have seen, for example, that 
in logical propositions we are concerned with both 
subject and predicate terms, and it has been made 
clear that our predicate terms must not only be 
predicable, but predicable of the objects denoted by 
our subject terms. If, for example, there should be 
anything indefinable, such a thing would correspond 
to what is called an individual ; and of such individ- 
ual it is obvious that we cannot affirm a genus and 
a differentia. Now, it is the difference between the 
views of Aristotle and Porphyry as to the kinds of 
thing that are capable of definition that accounts for 
the difference in their lists of predicables. Aristotle 
held that it is only as a universal or species that 
anything could be defined. Porphyry held that the 
subject of predication might be not only a species, 
but also an individual. It was, therefore, reason- 
able to include species in his list of predicables, for, 
doubtless, its species can be predicated of an indi- 
vidual ; but it would have been a mere tautology to 
predicate species of itself as would have happened 
if this predicable had been included in Aristotle's 
list. 

Our exposition of the doctrine of the predicables 
will follow in the main the Aristotelian view. We 



DEFINITION AND THE PREDICABLES 183 

shall assume that the subject terms of logical prop- 
ositions denote objects, or groups of objects, that 
are thought of as possessing attributes which ex- 
press the common nature of all the objects to which 
the subject term can be applied. Now if it is asked 
what can be predicated of objects so conceived, the 
answer is given in the list of Aristotelian predi- 
cates. Before, however, we consider in detail what 
each of these predicables means, we may point out 
that they are not all related to a subject in exactly 
the same way. Some of the predicables are com- 
mensurate with their subjects, and some are non- 
commensurate. To the former class belong defini- 
tion and proprium; to the latter, genus, differentia, 
and accident. 

The Commensurable Predicables. By a commen- 
surate predicable is meant one that is found wher- 
ever the subject of which it is predicated is found. 
It is an attribute, or group of attributes, that is 
always present when the object is present, and ab- 
sent when the object is absent. This class of pred- 
icables we shall explain briefly in this section. 

The definition we have considered already. It is, 
as we have seen, an answer to the question, What 
is it? and this question may be asked of anything, 
of an attribute as well as of a substance. For ex- 
ample, if we ask what acceleration is, and the phy- 
sicist were to answer, change of velocity per second, 
he is offering this as a definition, that is, a state- 
ment of what it is that makes anything the kind 
of thing called acceleration. Similarly, when an 



184 A TEXT-BOOK OF LOGIC 

organism is defined as a material body of which the 
parts are reciprocally related as ends and means, 
we should refuse to recognize as an organism any 
object which did not manifest these particular char- 
acteristics. The propositions, therefore, in which 
the predicate terms claim to be definitions are those 
in which the predicates also claim to be commensu- 
rate with their subject terms. This is only another 
way of saying, as we said above, that the state- 
ments which embody definitions must be capable -of 
simple conversion. The definition states what is 
essential to the existence of the objects denoted by 
the term that is defined. 

A proprium or property is an attribute peculiar 
to or characteristic of an object, and is commen- 
surate with its existence, but it is not an essential 
part of its definition. We may state the relation 
between the proprium and definition by saying that 
by means of the proprium we develop the meaning 
of a term from the point at which its definition 
stopped. From this it will be obvious that whether 
we go beyond the meaning that is assigned to a 
term in its definition will depend upon a motive 
other than that which makes definition necessary. 
In other words, the propria of terms are those char- 
acteristic features of an object's nature which re- 
main after definition has removed any existing am- 
biguity; and whether these are predicated as part 
of the term's meaning will depend upon whether 
special motives operate to make them explicit. For 
example, an equilateral triangle may be defined as 



DEFINITION AND THE PREDICABLES 185 

a three-sided plane figure having all its sides equal. 
This statement is sufficient for the purpose of dis- 
tinguishing this kind of triangle from all other 
kinds. But if we were interested further in equi- 
lateral triangles, we should find that they are also 
equiangular, and this fact of being equiangular is 
called a property of the kind of triangles in ques- 
tion. Likewise, contractility, irritability, assimilat- 
ing food, reproduction after its kind, are properties 
of an organism as this term was defined above. 

The Non-Commensurable Predicables. By a non- 
commensurate predicable is- meant any quality which 
alone does not exhaust the nature of an object, or 
which belongs to an object in some only of the ob- 
ject's relations. In neither case is the nature of 
the objects denoted by the term made entirely ex- 
plicit. The following illustrations will make this 
clear. 

We may, in the first place, predicate of any sub- 
ject the genus to which it belongs. That is to say, 
we may affirm the area of clear meaning of a term, 
and this may be all that is necessary to convey our 
meaning. It is obvious that we are here dealing with 
the class of cases that were considered above under 
the head of translation. But, as we saw there, the 
genus alone does not tell us all that is necessary 
for a complete understanding of any object's nature. 
The genus is, therefore, an incommensurable pred- 
icable. We may, in the second place, predicate of 
a subject its differentia, that is, that part of the es- 
sential nature of the subject which distinguishes it 



186 A TEXT-BOOK OF LOGIC 

from other species of the same genus. If, therefore, 
we are in danger of ambiguity from a tendency to 
confuse species, we may, to make our meaning clear, 
resort to the method of calling attention to the 
specific differences of the objects that we have hith- 
erto failed to distinguish. But the differentia alone, 
as we have seen, does not exhaust the nature of any 
object, and it is not, therefore, a commensurable 
predicable. In the third place, we may predicate 
some attribute not included in the definition of a 
subject, that is to say, an attribute that may or may 
not belong to the subject. For example, there is 
nothing in the nature of a pen that it should be 
made by a particular firm, or that it should belong 
to a particular person. These are accidental rela- 
tions, and belong to the pen merely as an individual. 
All such attributes, not contained in the definition 
or proprium, are called accidents. 

REFERENCES 

H. A. Aikins, The Principles of Logic, Ch. II., III. 

J. E. Creighton, An Introductory Logic, 3d Edition, Pt. I., 
Ch. V. 

J. G. Hibben, Logic Deductive and Inductive, Chs. IV., V. 

W. S. Jevons, Elementary Lessons in Logic, Lesson XII. 

S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
tion, Ch. V. 

W. Minto, Logic Inductive and Deductive, Pt. II., Chs. L, II. 

C. Read, Logic Deductive and Inductive, 3d Edition, Ch. 
XXII. 

W. J. Taylor, Elementary Logic, Chs. III., VI. 



DEFINITION AND THE PREDICABLES 187 



ADVANCED 

R. W. B. Gibson, The Problem of Logic, Chs. II., III. 

H. W. B. Joseph, An Introduction to Logic, Chs. IV., V. 

H. Lotze, Logic, Bk. II., Ch. I. 

J. S. Mill, A System of Logic, Bk. I., Chs. VII., VIII. 

F. C. S. Schiller, Formal Logic, Chs. V., VI. 

C. Sigwart, Logic, Pt. II., §§ 44. 

J. Venn, Empirical Logic, Ch. XL 

J. Welton, A Manual of Logic, Vol. I., Bk. I., Chs. III., V. 



QUESTIONS 

1. From what two standpoints may the logical discussion 
of terms be carried on, and to what new problems does 
such a discussion give rise? 

2. Define each of the problems enumerated in your answer 
to the previous question. 

3. Define the nature and limits of the demand for non- 
ambiguous statements. 

4. What is the practical importance of being able to make 
non-ambiguous statements? 

5. State and criticise the traditional doctrine of ambiguity. 

6. In what sense can ambiguity be said to be the funda- 
mental problem of logic? 

7. Explain the nature of translation as a method of over- 
coming ambiguity. 

8. What conditions call for the employment of translation 
in the removal of ambiguity? 

9. What conditions call for the employment of definition in 
the removal of ambiguity? 

10. Explain and illustrate: The method of definition is 
comparison. 

11. What is meant by: Logical definition is per genus et 
differ en ti am? 



188 A TEXT-BOOK OF LOGIC 

12. What do you understand by real and verbal definition? 
In what two senses may verbal definition be understood? 

13. What is the logical significance of the distinction of 
real and verbal definition? 

14. What is the relation of purpose to logical definition? 

15. In what two ways may our definitions fall short of 
being strictly accurate? 

16. Explain and illustrate how a definition may be too broad. 

17. Explain and illustrate how a definition may be too nar- 
row. 

18. How does the simple conversion of a definition guard 
against introducing anything superfluous into the defi- 
nition ? 

19. How may we guard against figurative language in defi- 
nitions? 

20. Explain: The terms of a definition should be more 
elementary than the term to be defined. 

21. What is meant by a circular definition, and how may 
circular definitions be avoided? 

22. What do you understand by a predicable? 

23. How many predicables are there, and what is the dif- 
ference between Aristotle's and Porphyry's lists of the 
predicables? 

24. What is the relation of the problem of the predicables 
to that of definition? 

25. Explain why Aristotle's and Porphyry's lists of the 
predicables differ? 

26. What is meant by a commensurable predicable? 

27. Which of the predicables are commensurable? 

28. In what sense is a definition a predicable? 

29. What is a proprium? 

30. What is meant by a non-commensurable predicable? 

31. Explain genus, differentia, and accident as non-com- 
mensurable predicables. 



DEFINITION AND THE PREDICABLES 189 



EXERCISES 

1. Write three ambiguous statements whose ambiguity can 
be removed by translation. 

2. Write three ambiguous statements whose ambiguity can 
be removed by definition. 

3. Define, and state, in each case, the purpose that the 
definition is intended to serve: anger, river, house, em- 
peror, metal, justice. 

4. Criticise the following definitions, and show what rules, 
if any, are violated by them: 

(1) Thunderbolts are the winged messengers of the 
gods. 

(2) Round is a quality that belongs to any rotund 
object. 

(3) Man is a vertebrate animal. 

(4) An inflammation is some abnormal condition of 
one of the body tissues. 

(5) An absentee is a person who does not live in his 
own country, or who does not look after his own 
property. 

(6) Prudence is the ballast of the moral vessel. 

5. Construct three definitions for the purpose of showing 
how definition depends upon comparison. 

6. To which of the Predicables does each of the following 
predicates belong : 

(1) The whale is a mammal. 

(2) The whale is a vertebrate. 

(3) The whale lives in the ocean. 

(4) The whale was caught and brought to land. 

(5) Logic is a good mental discipline. 

(6) The tiger is a predatory animal. 

(7) Englishmen are keen sportsmen. 

(8) Lord Shaftesbury was a great philanthropist. 

7. Give the genus, differentia, proprium, and accidens of 
(a) peninsula, (b) triangle, (c) affirmative statement. 



CHAPTER VII 

DIVISION AND CLASSIFICATION 

Relation of Definition and Division. Whenever 
ambiguity threatens any statement on account of 
the vagueness of the outlying range of a word's 
meaning, we may remove the ambiguity by defining 
the word's meaning. The method of definition, as 
we saw in the last chapter, is comparison. By this 
method we distinguish a meaning from one or more 
others with which we are in danger of confusing it, 
and our result is a division of the genus into two 
or more species. There is, however, nothing in the 
nature or conditions of definition that, in principle, 
assures us that all the distinguishable meanings of 
a genus have been discovered, and nothing, there- 
fore, that assures us that we have examined all the 
species which belong to the genus from which our 
definition starts. If, therefore, instead of asking 
how one species differs from another, we wished to 
know how many species there are in a given genus, 
we should be confronted with a new problem which 
it is the business of logical division to consider ; for 
by division we mean, in general, the method that 
must be employed to develop systematically all the 
species which belong to a genus. Now, if it is asked 
why any one should raise such a question as this, we 
can only say that the demand for non-ambiguous 
statements may be left unsatisfied after making the 

(190) 



DIVISION AND CLASSIFICATION 191 

meaning of our words as clear as possible. Ambi- 
guity, in other words, may be occasioned not only 
by uncertainty in the connotation of terms, but also 
by uncertainty in their denotation; and whenever 
there is vagueness in either respect there is likely 
to be a corresponding vagueness in the other. From 
this point of view, logical definition and division are 
closely connected problems, and they differ merely 
as one stage differs from another in a single process. 
In logical division we carry further the process that 
begins in logical definition, and the object is to re- 
move any remaining uncertainty in a word's mean- 
ing. 

What is Meant by Logical Division. The word 
'division' is not well chosen to designate the process 
that we have now to describe. If it should suggest, 
as it ordinarily must, that it is the method by which 
we split up a genus into its component parts, in 
much the same way that a house-wrecker separates 
the doors, windows, joists, etc., of the building he 
is dismantling, we should be misled entirely in our 
understanding of what the term means or the proc- 
ess implies. If this were the sense in which we were 
required to understand the word, its application 
would not give us a clearer apprehension of a term's 
meaning, but would result in the destruction of the 
meaning altogether. It will, perhaps, set the mat- 
ter in a clearer light if we say that logical division, 
like logical definition, starts with species or con- 
cepts, and that in both cases we are concerned with 
the kinds in which the species is found realised, 



192 A TEXT-BOOK OF LOGIC 

This being the case, we cannot say that a genus is 
the sum of its species; we can only say that it is 
differentiated into its species. 

In logical division, we are concerned with the 
relation of a genus and its species. But that rela- 
tion, as we have just seen, cannot be one of a whole 
to its parts; it is rather a relation in which the 
species disjunctively enumerate the alternatives 
which, when taken as an enumeration, denote the 
range of a term's meaning. That is, by division we 
analyse the denotation of a term's meaning. For 
example, if we should divide the genus 'rectangle' 
into two species, one with its adjacent sides equal, 
and the other with its adjacent sides unequal, we 
cannot mean by rectangle, in such a case, the sum 
of these two species. 'Rectangle' does not mean the 
square plus the oblong; it means either the square 
or the oblong. That is to say, the genus is realised 
in each of its species; the species of any genus ex- 
hibit distributively, not collectively, a word's mean- 
ing. 

If, now, we should seek to derive from these 
statements about the nature of logical division a 
rule which, when applied to any case, will serve as 
a test of the accuracy with which the division has 
been carried out, we may perhaps say that we must 
be able to predicate the genus, or whole that is di- 
vided, of each of the species of a logical division. 
Thus, in the previous example, we called the oblong 
a rectangle, and also the square a rectangle. Each 
is the whole of what a rectangle is. To take another 



DIVISION AND CLASSIFICATION 193 

illustration. The genus 'human being' may be log- 
ically divided into 'man,' 'woman,' etc., and the genus 
— human being — of which they are the species, 
may be predicated of each one, thus: 'a man is a 
human being/ 'a woman is a human being,' etc. 

In this discussion of the nature of logical divi- 
sion we have seen (1) that logical division is the 
process by which the range of a term's meaning 
can be exhaustively determined. It follows from 
this that the process, of logical division can be ap- 
plied only to what is in its nature general, in other 
words, to a species or concept. The genus, species, 
or concept to which the process of division is applied 
is called the totum divisum. We have seen also (2) 
that the sub-species of the whole that is divided 
enumerate disjunctively the kinds into which the 
whole is differentiated, that they are not the parts 
which when taken together constitute the whole. 
From this it follows (3) that we must be able to 
predicate of each kind the qualities connoted by the 
genus or whole that is divided. When this is not 
possible logical division has not taken place. 

Other Kinds of Division. It will help to keep the 
meaning of logical division distinct, if we describe 
the characteristics of other operations that go by 
the same general name of division. Of these, there 
are in particular three : metaphysical, physical, and 
verbal division. These are, like logical division, 
mental operations, but each serves a distinct pur- 
pose. The purpose of logical division, as we have 

13 



194 A TEXT-BOOK OF LOGIC 

seen, is to enumerate the kinds or species into 
which a genus is differentiated, or, what is the same 
thing, the kinds or species in which the qualities of 
the genus are realised. The purpose of metaphysical 
division is to distinguish the several attributes 
which are capable of being predicated of a genus. 
This kind of division obviously lies at the founda- 
tion of the problem of the predicables which was 
considered in the last chapter. For the problem of 
the predicables, as we saw, was concerned with the 
character of the attributes that could be predicated 
of any species. When, therefore, we divide a spe- 
cies into its genus, differentia, proprium and acci- 
dens, we are not employing what is technically 
known as logical division, but a method that is 
known as metaphysical division. The difference 
between these two methods may be brought out in 
the statement that in metaphysical division we 
must be able to predicate of the genus the species 
which our division has been the means of distin- 
guishing; whereas in logical division the converse 
statement holds true, that is, it is the genus which 
must be predicable of the species. For example, if 
we divide 'organism' into 'animals/ 'birds/ 'fishes' 
and 'reptiles/ we have a logical division, — a divi- 
sion which makes it possible to predicate of each 
species the genus which has been divided. If, on 
the other hand, 'organism' is divided into 'living 
creature,' 'capable of locomotion/ 'quadruped/ etc., 
this is called a metaphysical division, — a division 
which makes it possible to predicate of the genus 



DIVISION AND CLASSIFICATION 195 

each of the attributes which the division distin- 
guishes. The purpose of physical division is to anal- 
yse a whole or aggregate into the parts of which 
it is composed. Thus, we may divide 'horse' into 
head, legs, ears, tail, etc. This process is sometimes 
called physical partition. It is distinguished from 
the other kinds of division by the fact that neither 
parts nor wholes can be predicated of each other. 
For example, it is obvious that 'horse' is neither 
head, nor legs, nor ears, etc. ; nor can we say of 
any one of these that it is horse. Verbal division is 
sometimes mentioned as a separate form of division. 
It is used to denote the act of distinguishing the 
homonymous meanings of a word. For example, the 
word 'hand' may mean either 'a labourer' or 'an 
organ of the human body.' 

Fundamentum Divisionis. We have seen that the 
motive to logical division is found in the interest 
we have in determining the whole denotation of a 
term's meaning. Logical division is, therefore, the 
method by which we systematically develop the de- 
notation of terms whose meanings have been fixed 
by definition. It follows from this that we cannot 
divide a term whose meaning is unknown to us. 
This fact is frequently overlooked by the student, 
and he is apt to make the effort to put the method 
into operation in a case in which his knowledge of 
the totum divisum, or term to be divided, makes his 
failure a foregone conclusion. Logical division pre- 
supposes that the totum divisum has been given a 
meaning by logical definition. If, consequently, we 



196 A TEXT-BOOK OF LOGIC 

are required to determine the denotation of a term 
with whose connotation we are unacquainted, we 
must first determine the meaning of that term by 
the method of logical definition. While, therefore, 
logical division and logical definition are, as we 
have seen, closely related processes, each has a dis- 
tinctive role to play in the development of meaning. 
With this caution in mind, we pass to a statement 
of certain features of the method of logical division 
which throw light upon the significance of the proc- 
ess itself. What, we may ask, is the basis of divi- 
sion? On what principle or principles are we to 
proceed in any given case? By what are we to be 
guided in working out a logical division? The 
answer to such questions as these is usually given in 
an exposition of what logicians call the fundamen- 
tum divisionis. By a fundamentum divisionis is 
meant some characteristic of the totum divisum 
which, when systematically applied, develops differ- 
ences among its members. Or, as it is sometimes 
said, it is that aspect of the genus in respect of 
which its species are differentiated. If, now, the 
purpose of logical division is to develop differences 
in respect of which species may be differentiated, 
we shall have to seek in our definition of the totum 
divisum for some indeterminate attribute which 
can serve as the basis of our division. Now that 
there should be something indeterminate in a defini- 
tion will become perfectly clear if we recollect that 
all that a definition aims to give is a meaning relevant 
to the situation and purpose which made the defini- 



DIVISION AND CLASSIFICATION 197 

tion necessary. There is no such thing as a complete 
definition in any other sense than a relevant defini- 
tion. The only other sense in which we can speak 
of definitions being complete is that we are ac- 
quainted with all the known meanings of a word. 
But in that case we should not have a single defini- 
tion but a series of definitions; and, of course, all 
that we could say about that is that the series is 
complete, not that the definition is. If, consequently, 
our definition of a term enables us to make unam- 
biguous statements, that is all that we can expect 
of it; but it does not follow that the definition will 
be sufficiently determinate for carrying out a logical 
division. For example, 'man' has been defined as 
a rational animal, and, as a definition, it serves its 
purpose well enough. But if we consider the deno- 
tation of the term's meaning thus defined, we shall 
find that there is something indeterminate in the 
word rational, for rationality, as we all know, ad- 
mits of degrees. When, therefore, we assert of any 
individual that he is a man, that is, a rational ani- 
mal, we cannot be understood to imply a definite 
degree of rationality, but only some degree. If, 
however, we asked what degrees of rationality exist, 
we should have to adopt some standard of ration- 
ality, or state more carefully what we mean by 
rationality in our definition of man. This standard 
or statement would be, for the purpose of logical 
division, our fundamentum divisionis. With respect 
to this fundamentum divisionis, some individuals 
will meet the requirements it lays down, and these 



198 A TEXT-BOOK OF LOGIC 

we call normal ; others will fail to meet it, and these 
we call abnormal. In the latter class, we find some 
who fall below, and some who fall above the stan- 
dard : the sub-normal and the super-normal respect- 
ively. The sub-normal, again, may be divided into 
dements, those in whom mental deficiency appears 
subsequently to mental development, and aments, 
those who have never attained normal mental devel- 
opment. The aments may be divided, according to 
the degree in which they depart from the normal, 
into feeble-minded, imbecile, idiot. This division 
may be shown in tabular form as follows: 

Man 

. A .. 

f \ 

Normal Abnormal 



r \ 

Sub-normal Super-normal 



r \ t \ 

Dements Aments Genius 



Feeble-minded Imbecile Idiots 

We may point out in this connection that every 
division reacts upon the definition from which it 
starts to make it more exact. For example, we 
found the definition of man as a rational animal 
defective because it neither stated what is meant 
by rationality, nor what degrees of rationality were 
to be recognised. . Both these deficiencies are made 
good in logical division. Thus, to make our funda- 
mentum divisionis clear, we may say that by ration- 
ality we mean 'a degree of intellectual capacity suffi- 



DIVISION AND CLASSIFICATION 199 

cient to enable its possessor to perform his duties 
as a member of society in that position of life to 
which he is born/ and the classes of those who ful- 
fill these standard requirements or depart from 
them either by way of excess or defect are the 
normal, dements, feeble-minded, imbecile, idiot, 
genius. When, therefore, we look back upon the 
original definition from the standpoint of our 
completed division, it has taken on a more definite 
meaning. We now know not only what is specifically 
meant by calling any man rational, but we also know 
what are the different degrees in which rationality 
may in any case be realised. In other words, our 
division enables us to say that the concept 'man,' 
when determined with respect to rationality, may 
be realised in either one or the other of the forms 
specified in the division. 

Questions of Terminology. We shall postpone 
further discussion of the problems of logical divi- 
sion until we have explained the technical terms in 
which the discussion must be carried on. For the 
sake of completeness, we may recall that the term 
totum divisum was used above to denote the whole 
that is divided; it is the genus with which any 
division starts. When viewed in relation to all the 
species to which logical division gives rise, the 
totum divisum is called the summum genus. The 
species with which a division ends are called in- 
firmae species. If, as in the illustration used in 
the last section, our division is carried through a 
number of stages, the intermediate species, that 



200 A TEXT-BOOK OF LOGIC 

is, those that fall under the summum genus, are 
spoken of as subaltern genera. When, however, 
we wish to point out the relation that any one of the 
subaltern genera has to the next below it in the 
series, we designate this subaltern genus the prox- 
imum genus. It will be observed that the totum 
divisum is a proximate genus with respect to the 
next below it in the series, but a summum genus 
with respect to all, — whether one or more, — that 
lie below it in the series. The constituent or co- 
ordinate species are those which are differentiated 
at any single stage in the process of logical division. 
These distinctions, it should be noted, are purely 
relative, and the student will have no difficulty in 
mastering the terminology if he observes that they 
all hinge upon the meaning assigned to genus and 
species. A genus is anything considered as a sub- 
ject of division, and a species is always the end- 
product of a division. The same thing, therefore, 
may be both a genus and a species, but whenever 
that is the case, the same thing is being looked at 
from different points of view. 

Rules of Logical Division. There are other fea- 
tures of logical division than those that have been 
already considered with which it is important that 
the student should become acquainted. These we 
shall state and illustrate in connection with our 
enumeration and exposition of the rules of logical 
division. 

The first rule is that a logical division must pro- 
ceed in all its stages upon one fundamentum divi- 



DIVISION AND CLASSIFICATION 201 

sionis. The reason for this, of course, is found in 
the nature of the problem that logical division is 
set to solve. That problem is to develop the mean- 
ing of a term so as to make determinate whatever 
may have been left indeterminate in its definition. 
If we did not keep within that aspect of a term's 
meaning with which our logical division starts, 
we should fail to develop this meaning from an in- 
determinate to a more determinate form. In the 
example used above, we found that a number of de- 
grees of rationality exist, and that these must be 
included in our definition of 'man' if this concept is 
to be completely determined. If we had found, in 
our division of the term, species of another kind, — 
let us say red man, yellow man, — it would be evi- 
dent that we had gone outside the fundamentum 
divisionis, rationality, and that we had consequently 
failed to determine that aspect of the term's meaning 
with which we were concerned. Whenever this hap- 
pens, whenever, that is, we fail to carry the division 
through on a single principle, we are said to have a 
cross division. All the species to which a logical 
division gives rise must be the same in kind; and 
this is possible only if we retain the same principle 
of division throughout. Again, in carrying out a 
principle of division, we aim to make our species 
exclusive, to include, that is to say, in any one species 
only that which is definitely excluded by the other 
co-ordinate species. The constituent species of a 
genus must not overlap. This requirement is ob- 
viously related to that feature of a logical definition 



202 A TEXT-BOOK OF LOGIC 

which emphasises the difference between two or 
more conflicting meanings (differentia), as the 
former requirement connects logical division with 
the other aspect of definition which emphasises the 
common likeness of these conflicting meanings 
{genus) . 

It is not difficult to apply the first rule of divi- 
sion when the fundamentum divisionis is completed 
in a single step. For example, if 'man' is defined as 
'a rational animal possessing a skin-color of some 
kind,' the latter part of the definition may become 
for us a principle of division. Dividing man then 
according to skin-colour we find the denotation of 
the term to be as follows : 

Man 

A 



White man Black man Yellow man Brown man Red man 

When, however, the division is carried through 
several stages, as it frequently is, it may not be 
apparent how a single principle can control the 
whole series of divisions. If, for example, we were 
to divide 'human being' into 'male' and 'female,' and 
were then to divide 'female' into 'brunette' and 
'blonde/ it is obvious that the fundamentum divi- 
sionis in the first division is sex difference, and in 
the second, complexion colour. In cases like this, 
we cannot look upon the division as a series which 
develops a single theme; we must regard it rather 
as a chain of discontinuous divisions which contains 
as many separate divisions as there are distinct 
fundamenta. The fact that they can be written 






DIVISION AND CLASSIFICATION 203 

consecutively does not have any logical significance ; 
the reason for giving this form to them is econom- 
ical; it saves time, when the end product of one 
division is the starting-point of a new one, to con- 
tinue in the serial order. If, however, our practice 
were guided by logical requirements, we should re- 
write our term whenever we intend to apply to it a 
new principle of division. 

Let us now consider the case of a division which 
has the characteristics of a continuous series, that 
is, a series which develops a single idea through a 
number of stages. The significance of this case is 
that it emphasises the importance and illustrates 
the method of systematically developed knowledge, 
of knowledge, that is, which proceeds at each step by 
the smallest possible degrees of relevant difference. 
Thus, in carrying out a division which develops its 
meaning in a continuous series, we are counselled to 
make the steps of the series as small as possible. This 
is the purport of the Latin injunction, Divisio ne fiat 
per saltum: you must not make your division go 
by leaps. A division that is not systematically de- 
veloped is useless for the purpose that put it in oper- 
ation. But since, throughout all the stages that we 
carry our division, we need to be guided by a single 
principle, it is evident that at each stage of the divi- 
sion we must use a fundamentum divisionis that is 
some modification of the principle with which we 
began the division. That is to say, each subordinate 
fundamentum must fall within the meaning of the 
original fundamentum. An illustration, borrowed 



204 A TEXT-BOOK OF LOGIC 

from Gibson, will make this evident. Let us take 
as our fundamentum divisionis, the side-relations of 
'quadrilateral figures/ understanding by quadrilat- 
eral figure 'a plane rectilinear quadrilateral figure.' 
Our purpose is to develop the number of types which 
belong to this class. According to their side-rela- 
tions, 'quadrilateral figures' are either 'parallelo- 
grams,' that is, figures whose opposite sides are 
parallel and equal, or 'non-parallelograms.' Divid- 
ing these species further according to the inclination 
of their sides, a special form of the original funda- 
mentum, we get, in the case of the parallelograms, 
rectangle and non-rectangle ; and in the case of the 
non-parallelograms trapezium, a figure in which 
there are no parallel sides, and trapezoid, a figure in 
which two of the sides are parallel but not equal. 
Another specification of the original fundamentum 
would be relative side-length. If we apply this to 
rectangle we get square and oblong; and to non- 
rectangle, rhombus and rhomboid, oblique figures 
which correspond to the square and oblong respect- 
ively. All these relations expressed in the form of 
a genealogical tree are as follows: 

Quadrilateral Figure 



A. 



r > 

Parallelogram Non-parallelogram 

. A „ , A „ 

f N f "S 

Rectangle Non-rectangle Trapezium Trapezoid 

A 



Square Oblong Rhombus Rhomboid 



DIVISION AND CLASSIFICATION 205 

The second rule is that a logical division must 
be exhaustive. The reason for this rule is connected 
obviously with the purpose that controls such divi- 
sion, namely, to denote in orderly relation whatever 
belongs to a certain genus. What the rule states 
is that a place must be found, when the division has 
been made, for everything that belongs to the genus 
in one or other of the constituent species. It is only 
another way of stating the purport of the rule to 
say that the constituent species together must be 
coextensive with the whole genus. The rule is in- 
tended to guard against too narrow and too broad 
division. When the division is too narrow some- 
thing is omitted from, and when the division is too 
broad something is added to, the genus, and which- 
ever fault we may fall into, the division is rendered 
useless. Instances of too narrow division are : 'men' 
into 'good' and 'bad;' and 'objects' into 'useful' and 
'ornamental.' Too broad division is likely to occur 
whenever there is an indistinct apprehension of the 
connotation of the terms we employ in our divisions. 
Unless, therefore, a division is exhaustive, that is, 
neither too narrow nor too broad, we have not really 
divided at all ; for when the division is too narrow, 
the constituent species are equivalent to only part of 
the genus, and when it is too broad, they are equiv- 
alent to the genus and something else. Whenever a 
genus has been properly divided, the denotation of 
genus and species must exactly coincide. 

Dichotomy. Our discussion of logical division 
has emphasised two things: (1) that our ability to 



206 A TEXT-BOOK OF LOGIC 

use the method depends upon our knowledge of the 
subject to which it is applied, and (2) that to insure 
against omitting anything that really belongs to a 
genus we must make our division exhaustive, and 
that when this requires us to carry the division 
through several stages, the steps between one sub- 
division and another must be made as small as pos- 
sible. Division is not, consequently, an easy method 
to apply, although it is not difficult to understand; 
but the difficulty is due primarily to the great com- 
plexity of the material that nature presents for our 
study. 

Dichotomy is a traditional method of division 
which has been supposed to relieve us of the diffi- 
culties to which we have just referred, and to make 
it possible, in the absence of any considerable knowl- 
edge of the subject under investigation, to deter- 
mine the species which may belong to it. If this 
were true, we might omit the consideration of it 
entirely on the ground that it is a merely formal 
process ; if it is not true, we must consider its value 
in relation to our effort to make our knowledge of 
things systematic. That it is not true is the position 
of modern logicians as it was of Aristotle. We must, 
therefore, place this method in its relation to our 
foregoing discussions. 

First, let us inquire how dichotomy differs from 
the form of division which we have just considered. 
The characteristic of a dichotomous division is, as 
the name implies, that it proceeds at each step of 
the division by dividing a genus into two alternative 



DIVISION AND CLASSIFICATION 207 

species. Now, if each step of such a division ex- 
hausts the genus we are dividing, it is apparent that 
one of the terms must be an indefinite or so-called 
negative term. Thus, if we divide 'triangle' accord- 
ing to the relations of the sides, we shall have at 
the first division, if we take equality of all the sides 
as the fundamentum, two species, 'equilateral' and 
'non-equilateral.' Dividing the 'non-equilateral' 
term with reference to the equality of two of the 
sides, we shall have once more two species, 'isosceles' 
and 'non-isosceles.' If we divide now the 'non- 
isosceles' term on the basis of the only remaining 
possibility, namely, the equality of one side with 
itself, we get also two species, 'scalene' and, if there 
are any, 'non-scalene.' The arrangement of these 
divisions in a tree will illustrate the typical form 
of division by dichotomy. Thus : 

Triangle 
Equilateral Non-equilateral 

. A ^ 



Isosceles Non-isosceles 

A 



Scalene Non-scalene 

From the foregoing statements and illustration, 
it will be apparent that we cannot begin to divide 
a term by dichotomy without having before our 
minds some definition of the genus that we wish to 
divide. Unless we knew, for example, that a tri- 
angle was 'a plane figure bounded by three straight 
lines,' we should not be able to divide it to determine 



208 A TEXT-BOOK OF LOGIC 

its species. Dichotomy, as much as any form of divi- 
sion, presupposes definition. Now, the connection 
between dichotomy and definition per genus et differ- 
entiam, may be expressed by saying that every such 
division suggests a definition of the class we are 
dividing, and that every definition implies a division 
by dichotomy. Thus, to take the illustration already 
used, a 'triangle' may be defined as 'a three-sided 
plane figure whose sides have a certain relation to 
each other;' and if we wish to make the indeter- 
minate part of this definition determinate, we divide 
by dichotomy in order to bring out the specific rela- 
tionship of the sides to each other. 

We may observe, further, that, applied to rela- 
tively simple cases, dichotomy is a rather cumber- 
some method of doing what can be accomplished 
more expeditiously at a single step. There is no 
reason, for example, why we should not divide tri- 
angle into its constituent species at once ; for, in such 
a case, it is not by the method of division, but by 
reason of our acquaintance with the subject-matter, 
that we know the species that our division is a means 
of classifying. We may also observe that it is un- 
avoidable in division by dichotomy that the end- 
product should be a hypothetical term, — 'non- 
scalene' in the case above — on the existence or non- 
existence of which the division itself can throw abso- 
lutely no light. 

What now, it may be asked, is the value of a 
division by dichotomy? It is valuable in the first 
place as a test of the accuracy and exhaustiveness 



DIVISION AND CLASSIFICATION 209 

of our analysis of a term's meaning. To take an 
illustration from Aristotle, we may classify the 
Predicables as follows: 

Predicables 



r \ 

Commensurable Non-commensurable 



f \ r ~\ 

Essence Not essence Part of essence Not part of essence 

(Definition) (Proprium) (Genus or Differentia) (Accidens) 

It will be noticed in this case that the fundamentum 
divisionis, or, as we may say, the differentia, is the 
relation of the species according to the degrees of 
the essential connection that they severally have to 
the genus, and that the division is throughout dich- 
otomous. But, of course, the Predicables were al- 
ready known before they could serve as an illustra- 
tion of how dichotomy may verify a classification. 

We may also point out that a division by dich- 
otomy is also valuable if we wish to ascertain the 
position of a particular species in the class to which 
it belongs. Thus, to quote Welton, "in the Analytic 
Key prefixed to Bentham's British Flora, which is 
intended to enable anyone who has a specimen of a 
certain plant before him to discover its species and 
its technical name, the arrangement is nearly en- 
tirely dichotomous, and, for such a purpose, this 
form is the most useful. But to adopt dichotomy as 
a final arrangement would be absurd. A botanist, for 
example, starts at once with three classes of the sum- 
mum genus plant, viz., exogens, endogens, and acro- 

14 



210 A TEXT-BOOK OF LOGIC 

gens, and each of these is sub-divided into varying 
numbers of orders, and these again into still further 
varying number of genera, and so on, with little or 
no regard to dichotomy, the object being to make the 
classification agree with the distinctions existing 
in the plants themselves." 

The Tree of Porphyry. In a typical division by 
dichotomy, as we saw in the last section, it is the 
negative or indeterminate term that lends itself to 
further division. If, now, the division proceeds 
through all its stages by the dichotomous division 
of the positive or determinate term, we have a spe- 
cies of division which is illustrated by what is tech- 
nically known as the Tree of Porphyry.' An illus- 
tration will show not only the possibility of such a 
division, but exhibit the form that is characteristic 
of it. Thus: 

Substance 



Corporeal Incorporeal 

A 



Animate Inanimate 

A 



r 

Sensible Insensible 



Rational Irrational 

In any case of division by dichotomy whether of 
this type or not, the indeterminate or negative term 
and the determinate or positive term, in their rela- 
tion to each other, are sometimes referred to as 
Contradictory Opposites, Contradictory Relatives, 
or Contradictories. This designation is apt to be 



DIVISION AND CLASSIFICATION 211 

misleading unless it is pointed out that contradic- 
tion can be logically postulated of terms only when 
these have a common or underlying basis. There is 
no contradiction, for example, between virtue and 
beef-steak, because they do not belong to the same 
universe of discourse, that is, because they have no 
common basis. Animate and inanimate are contra- 
dictories because they are the alternative ways in 
which corporeal substance is capable of getting itself 
expressed. The alternative species, therefore, to 
which a dichotomous division gives rise may be 
spoken of as contradictory in the sense that they 
are the definite and exclusive forms in which the 
genus to which they belong is realised. It would, 
perhaps, avoid all ambiguity if we spoke of the rela- 
tion between the determinate and indeterminate 
terms of a logical division as Complementary. If 
we did so, we should have to mean that the indeter- 
minate term included within it all of the denotation 
of the genus that was not definitely included in the 
determinate term. Only on this interpretation can 
these terms be regarded as the names of alternate 
species. 

It will be observed that in a division of the type 
illustrated by the Tree of Porphyry the indetermin- 
ate term is rejected at each of the subordinate steps. 
This fact is technically known as an abscissio in- 
finite i r ; "hw 

Classification Defined. One does not need to go 
to text-books of logic to become acquainted with the 
process that is denoted by the term classification. 



212 A TEXT-BOOK OF LOGIC 

Before he has entered the university, nay before he 
has entered the common school, the normal child 
has learned to arrange the objects with which he is 
brought daily into contact into groups, and to do 
this on the basis of their observed likenesses and 
unlikenesses. Whenever anyone groups objects to- 
gether on the ground of their likenesses, and dis- 
tinguishes between groups on the ground of their 
differences, he is employing the method of classifi- 
cation. Classification, therefore, may be defined as 
the process of thinking together a number of objects 
on the ground of their common attributes, and of 
thinking apart groups of objects whose attributes 
are different. 

Classification and Definition. It will be seen that 
classification, as thus defined, is closely related to 
definition. Definition completes the process that is 
begun in classification. Classification underlies the 
defining process. This relationship will become evi- 
dent if we recall that definition aims to place the 
object whose meaning is not clear in a class with 
other objects which share with it a common set of 
attributes. When, therefore, we ask how we can 
find the genus of any term we wish to define, the 
answer will point us to the method of classification 
which we are now studying. This is only another 
way of saying, with a slightly different emphasis, 
what was said in the last chapter, namely, that the 
method of definition is based upon the comparison 
of the object we are defining with other objects that 
are in danger of being confused with it. Compar- 






DIVISION AND CLASSIFICATION 213 

ison is common both to definition and to classifica- 
tion. But we compare objects with each other in clas- 
sification for the purpose of ascertaining their com- 
mon attributes; in definition, we compare the ob- 
jects of a class for the purpose of discovering the 
differences which keep the sub-classes distinct. This 
statement has important practical and philosophical 
bearings. It enables us to see, for instance, how 
groups of objects can be considered as a single ob- 
ject, a fact that gives significance, as we have seen, 
to the general concrete term. Whenever we over- 
look the differences between the objects of which 
a class is composed, and emphasise the points of 
likeness by which each object retains its place in 
the class, we have constituted of the class a distinct 
kind of object. In such a class the individuals are 
no longer important, there is no discernible differ- 
ence between one and another ; they are, as Leibnitz 
would say, identical. But if, for any reason, the 
statements we make were dependent for their clear- 
ness upon the differences in the class, we should 
have to go beyond the method of classification by 
which our classes are constituted, and we should be 
forced, as we have pointed out, to adopt the method 
of definition. In classification, we are interested in 
the likenesses, in definition, in the differences of 
objects. 

Classification and Division. Whenever we are in 
danger of overlooking the distinctions that exist 
within a genus, whenever, that is, we are in danger 
of making ambiguous statements through our fail- 



214 A TEXT-BOOK OF LOGIC 

ure to keep in mind the whole denotation of a term, 
there exists a situation that may be relieved by the 
employment of the method of division. The starting 
point of a logical division is the genus, the whole 
which is possessed of a number of common qualities ; 
and the purpose of division is to mark out within 
the genus the species which realise, in different 
ways, these common qualities. The movement of 
thought is downward from the more general to the 
less general. If now we consider the characteristics 
of a classification, we shall find that they are the 
reverse of this. The situation in which we feel 
obliged to classify is one in which we are in danger 
of failing to observe the likenesses of objects on 
account of the prominence that their individual 
attributes have come to assume. Popularly ex- 
pressed, we are exposed to the danger of "missing 
the wood for the trees." The starting point of all 
classification, therefore, is the particular, the objects 
which are kept distinct and apart on account of 
their differences ; and the purpose that classification 
is intended to serve is to detect within these differ- 
ences certain relatively permanent groups of qual- 
ities. Our most available method for doing this is 
comparison; but that in respect of which the com- 
parison is made is determined by the interest that 
our classification is to promote. For instance, we 
may classify objects with respect to their use or 
with respect to their sense-attributes. It is the 
character of our interest in things that determines 
which of these principles of classification we choose ; 



DIVISION AND CLASSIFICATION 215 

but, in any case, the movement of thought in class- 
ification is upward from the particular to the gen- 
eral. Classification is the beginning of a process 
that we shall study more in detail when we come to 
the problem of induction. 

Kinds of Classification. It has been customary 
to distinguish two kinds of classification, — the arti- 
ficial and the natural. By an artificial classification 
is usually meant one in which the grouping of ob- 
jects takes place on the ground of their possessing 
some attribute or group of attributes which does not 
serve as the basis of any further statement about 
these objects. We may, for example, classify cer- 
tain objects of domestic furniture as chairs; but 
having done so, we are not able, on that basis, to 
predicate anything further of the objects to which 
the name chair is given. By a natural classification 
is generally meant one that groups objects on the 
ground of their possessing an attribute, or group of 
attributes, which serves as the basis of further pred- 
ication. For example, if we classify a group of ani- 
mals as mammals, we are able to say, by virtue of 
the fact that they are mammals, that they are also 
vertebrates. This view has received, among modern 
writers, a classic expression by Mill. It is based 
upon the supposition that there exist in nature 
classes of objects which are distinct from each other, 
and that if we make the differences of these classes 
the basis of our classification, we shall thereby mark 
off the 'natural kinds' from others which by way of 
contrast may be called artificial kinds. 



216 A TEXT-BOOK OF LOGIC 

Since the spread of the doctrine of evolution, it 
is no longer possible to maintain, in all fields of 
knowledge, the distinction of natural and artificial 
kinds. We no longer think of species of animals, 
for example, as marking fixed and distinct differ- 
ences between groups of objects; we have to think, 
according to the doctrine of evolution, of the whole 
animal series, from amoeba to man, as having 
sprung from a common ancestor. Species are not, 
in the meaning of the distinction we are now con- 
sidering, separate and distinct kinds. 

But while we no longer find it possible to classify 
objects in the way just considered, the distinction 
between natural and artificial suggests a truth of 
which we may take advantage in our discussion of 
this topic. The fallacy that underlies the separation 
of classes into natural and artificial seems to be, 
from the logictl standpoint, that it denies that rele- 
vancy to purpose is a factor in all classification. The 
classification of objects, for example, as natural is 
based on the supposition that the attributes of spe- 
cies are determined wholly by the nature of the ob- 
jects themselves, and that they are in no way and to 
no extent determined by the interest which prompts 
us to classify; while the classification of objects as 
artificial is predominantly, if not wholly, determined 
by the interest that controls the classification. This 
can not be maintained. For, as we have seen, knowl- 
edge is always the product of both kinds of factors, — 
of both subjective purpose and objective fact. And 
it is this analysis of what we mean by knowledge 



DIVISION AND CLASSIFICATION 217 

that gives us the clue to the distinction of natural 
and artificial kinds, and which enables us to under- 
stand the two main kinds of classification. Our 
classification does not depend upon the presence or 
absence of interest, but upon the particular kind of 
interest which we seek to satisfy. We may be in- 
terested, for example, in grouping objects according 
to their essential attributes, that is, according to 
the attributes which constitute them members of a 
class. We may also be interested in grouping ob- 
jects according to their non-essential attributes, 
that is, according to the attributes which are either 
implied by their essential attributes, or which are 
only accidental ones. In view of our discussion of 
the Predicables, this statement means that we may 
make the qualities which characterise the genus the 
principle of classification; or the qualities which 
characterise the proprium, or the accidens, the basis 
of classification. 

Classification according to the essential attri- 
butes of the objects compared gives a theoretical 
classification; and classification according to the 
non-essential attributes, a practical classification. 
In the former case, the theoretical interests which 
prompt us to study the nature of things are upper- 
most ; and in the latter, the practical interests which 
are concerned with the uses of things are in control. 
To take an illustration usually found in text-books 
of logic, the Swedish botanist, Karl Linnaeus (1707- 
1778) , based his classification of plants upon the 
comparison of the sexual organs of plants. The 



218 A TEXT-BOOK OF LOGIC 

distinct advantage of this method was that it made 
possible the indexing of plants in a convenient way 
into genera and species so that their relative posi- 
tion to each other in a series could be made out. 
This must be taken not as a theoretical, but as a 
practical classification, and, in principle, is not differ- 
ent from the arrangement of words in a dictionary 
in their alphabetical order. If, on the other hand, 
we make a classification according to the natural 
relationships of the species, we shall have an illus- 
tration of a theoretical classification. It will be 
obvious that many variations are possible within 
these two divisions ; but for the details, the student 
is referred to the larger books on logic and the 
principles of science. 

REFERENCES 

H. A. Aikins, The Principles of Logic, Ch. IV. 

J. G. Hibben, Logic, Deductive and Inductive, Ch. VI. 

S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
tion, Ch. V. 

W. Minto, Logic, Inductive and Deductive, Ch. IV. 

C. Read, Logic, Deductive and Inductive, 3d Edition, Ch. 
XXI. 

W. J. Taylor, Elementary Logic, Pt. II., Ch. V. 

ADVANCED 

R. W. B. Gibson, The Problem of Logic, Chs. IV., V. 

H. W. B. Joseph, An Introduction to Logic, Chs. III., V. 

F. C. S. Schiller, Formal Logic, Chsi IV., VI., §§ 6-10. 

C. Sigwart, Logic, Pt. II., §§ 42-43. 

J. Venn, Empirical Logic, Chs. XII., XIII. 

J. Welton, A Manual of Logic, Vol. I., Bk. I., Ch. VI. 



DIVISION AND CLASSIFICATION 219 

QUESTIONS 

1. In what way is logical division related to logical defini- 
tion? 

2. Name one way in which logical division may not be in- 
terpreted. 

3. Explain: By division we analyse the denotation of a 
term's meaning. 

4. What is meant by saying that the species enumerated 
in a logical division are to be read disjunctively? 

5. What is the test of a logical division? 

6. What is a metaphysical division, and how does it differ 
from a logical division? 

7. What do you understand by a physical division? Illus- 
trate. 

8. What is a verbal division? 

9. Define a fundamentum divisionis. 

10. Explain how one discovers for a particular division an 
appropriate fundamentum divisionis. 

11. In what respects can a logical definition be improved 
from the standpoint of logical division? 

12. Explain the following terms: genus, species, totum di- 
visum, summum genus, infirmae species, subaltern 
genera, proximate genus, constituent species. 

13. What is the first rule of logical division? 

14. What is a cross division? Explain how it occurs. 

15. What is meant by saying that the species to which a 
logical division gives rise must be exclusive? 

16. What are the character and importance of a continuous 
series? 

17. How can we keep within a single fundamentum when 
our division is carried through a number of stages? 

18. State and explain the second rule of logical division. 

19. What difficulties in the method of logical division are 
supposed to be met by dichotomy? 

20. What are the characteristics of a dichotomous division? 

21. What is the relation of dichotomy to definition? 



220 A TEXT-BOOK OF LOGIC 

22. What advantages are sometimes claimed for a dich- 
otomous division? 

23. What is the Tree of Porphyry? 

24. What do you understand by contradictory opposites? 

25. Explain absdssio infiniti. 

26. What is classification? 

27. How are classification and definition related? 

26. What is the relation of classification and division? 

29. State Mill's doctrine of classification. 

30. Why has the distinction of natural and artificial kinds 
broken down? 

31. What is the relation of purpose to classification, and 
what effect does this have upon the distinction of nat- 
ural and artificial classification? 

32. What bases of classification may be recognized as im- 
plicit in Mill's doctrine of classification? 

33. Explain theoretical and practical classification. 

EXERCISES 

1. Divide logically the following terms, stating in each in- 
stance (a) the definition and (b) the fundamentum di- 
visionis. 

psychology gun culture 

European student government 

2. Examine the following divisions, and point out which 
rule of logical division, if any, is broken by them: 

(1) Substances into material and spiritual. 

(2) Books into scientific, philosophical, and literary. 

(3) Religions into true and false. 

(4) Students into those who are diligent, female, and 

athletic. 

3. What is the metaphysical division of the following 
terms? 

landscape philosophy toy 

capital child amusement 



DIVISION AND. CLASSIFICATION 221 

4. Divide physically six terms of your own selection. 

5. Give six illustrations of verbal division. 

6. Illustrate a cross division, and explain how it is brought 
about. 

7. Give two examples of dichotomy. 

8. Illustrate by two examples the Tree of Porphyry. 

9. Give examples which illustrate the characteristics of 
(a) a theoretical and (b) a practical classification. 



CHAPTER VIII 

CATEGORICAL PROPOSITIONS 

Types of Propositions. In a former chapter we 
saw that predication is the act of affirming or deny- 
ing something (P) of something else (S). Any 
statement which rests upon predication, that is, 
which affirms or denies something of something else, 
is called in logic a proposition. Predication may be 
of various degrees of directness or explicitness, ac- 
cording to the degree of our knowledge of the sub- 
ject of predication. For example, if my knowledge 
of natural history is only slight, I shall probably be 
able to say of a given animal merely that it is either 
a lion or a tiger or a leopard or something else. If 
a further study of animals makes me acquainted 
with the characteristics of the species lion, I shall 
then be able to say that if a given animal has these 
characteristics, it is a lion. If, again, the examina- 
tion of a particular animal showed that it does or 
does not have these distinguishing qualities, I should 
then be able to say that it is or is not a lion. The 
forms of predication illustrated in these instances 
we have learned already to call alternative, hypo- 
thetical, and categorically respectively. The state- 
ments in which these forms of predication are ex- 
pressed are called disjunctive, hypothetical and cate- 
gorical propositions. The classification of proposi- 
tons into disjunctive, hypothetical, and categorical 

(222) 



CATEGORICAL PROPOSITIONS 223 

is said to be made from the standpoint of relation, of 
the relations, that is, that obtain between the ele- 
ments that enter into the proposition. It is quite 
obvious, for instance, that the predicate and subject 
of each of the above propositions dealing with what, 
under given conditions, can be predicated of a par- 
ticular animal, are related in quite distinct ways. 
The predicate term is asserted differently in each 
case, and it is this difference in our manner of 
asserting that lies at the foundation of the distinc- 
tion we make between disjunctive, hypothetical, and 
categorical propositions. The form of assertion 
corresponds to a real element in the knowledge that 
an assertion claims. We have shown this in detail 
in the chapter on propositions. Our present task 
is to study the various kinds of propositions and the 
logical problems to which they give rise. In the 
present chapter, we shall consider a number of ques- 
tions which relate to simple predication and w T hich 
throw light upon the nature of categorical state- 
ments ; in the next, we shall consider problems con- 
nected with the other forms of the proposition. 

Classification of Categorical Propositions. The 
possibility of a classification of categorical proposi- 
tions, that is, propositions which predicate P of S 
simply, rests upon the fact that unconditional state- 
ments (1) do not always, but sometimes do, apply 
to a determinate part of the subject-matter of such 
statements; or (2) do not always, but sometimes do, 
unite the predicate with the subject of such state- 
ments; or (3) do not always express the same de- 



224 A TEXT-BOOK OF LOGIC 

gree of certainty. We shall illustrate each of these 
cases in the order in which they have been named. 
As an illustration of the first case, where the state- 
ment applies to an indeterminate part of the subject- 
matter of the statement, let us take 'Not all men are 
honest who say they are.' This is a proposition in 
which honesty is predicated of some only of the men 
who declare their honesty. As an illustration of the 
second case, where the statement does not unite the 
predicate with the subject of the proposition, let us 
take the illustration just used and observe that hon- 
esty is denied of some of the individuals who assure 
us that they are honest. As an illustration of the 
third case, where our statements express different 
degrees of certainty, let us take the following: 'He 
may be honest though poor;' 'He is honest but 
poor;' 'He must be honest.' 

The three characteristics of propositions just 
mentioned and illustrated are so constant, and they 
occur in such a wide range of our knowledge, that 
early in the history of logic it was found necessary 
to distinguish them by the use of technical terms, 
that is, by terms which mean, whenever they are 
used, just these characteristics of propositions. 
Thus, when we wish to call attention to the fact that 
our statements do or do not apply to a determinate 
part of the subject-matter of the proposition, we 
are said to be dealing with the proposition from the 
standpoint of its Quantity. When, on the other 
hand, we wish to emphasise the fact that the pred- 
icate does or does not belong to the subject, we are 



CATEGORICAL PROPOSITIONS 



225 



said to be dealing with the proposition from the 
standpoint of its Quality. When, thirdly, we wish 
to distinguish the degree of certainty that attaches 
to our statements, we are said to be dealing with 
the proposition from the standpoint of its Modality. 
If to this statement we now add what was said 
in the first paragraph of the present chapter about 
the degrees of explicitness in predication being made 
from the standpoint of Relation, we have before us 
the four ways in which propositions may be class- 
ified. We shall now write down, for reference, the 
classification of propositions when looked at from 
each of the above-mentioned points of view. 

RELATION 

Categorical 

Hypothetical 

Disjunctive 



QUANTITY 

Singular 
Universal 
Particular 
Indesignate 



QUALITY 

Affirmative 
Negative 



MODALITY 

Assertoric 
Necessary 
Problematical 



Quantity of Propositions. The problem of the 
quantity of propositions is one which is concerned 
with the question whether we intend our statements 
to be true of a determinate or indeterminate part 
of the subject-matter of such statements. It is, for 

15 



226 A TEXT-BOOK OF LOGIC 

example, quite clear that when any one says, 'I have 
seen Paris/ he is ordinarily understood to mean that 
he has been to Paris, and visited some of its im- 
portant boulevards, churches, galleries, etc. No one 
would understand him to mean that he had become 
acquainted with the whole of Paris. The truth of 
the claim to have seen Paris would be that some 
unspecified parts of Paris had been visited. Again, 
no one who made the above statement would ordi- 
narily wish to be understood that he had a thorough 
acquaintance with those parts of Paris which had 
come under his observation. The statement is in- 
tended to claim an acquaintance, such as it is, with 
certain parts of the French capital. From these 
considerations, it is quite evident that the statement, 
'I have seen Paris,' leaves undetermined both the 
range and the thoroughness of the observation that 
is claimed by the statement. Now, although a great 
number of the statements we make about even the 
most familiar and ordinary events of life are, in the 
sense of these illustrations, quite undetermined, we 
sometimes make statements which we intend to be 
understood with no such limitation. To take a sim- 
ple illustration, if one were asked, 'What is the most 
direct route from Chicago to London?' the answer, 
if one were given, would claim to be determinately 
true of the subject of the inquiry, either of a speci- 
fied part of the inquiry or of the whole of it. For 
instance, the reply might take this form, 'Go by way 
of the New York Central lines to New York, and 
then inquire;' or it might take this form, 'Go to 



CATEGORICAL PROPOSITIONS 227 

New York, and then take passage with the Cunard 
Line to London via Liverpool.' Let us take another 
illustration. A mathematical problem is an inquiry 
of a definite kind, and we may work the problem 
up to a certain point quite sure that all the steps 
we have taken lead us toward the true solution of 
the whole problem. We may or we may not be able 
to proceed beyond that point. The fact that we can- 
not, does not invalidate the claim that we may make 
of having solved a definite part of the problem. That 
is to say, if the answers we make to questions, and 
the statements in which we express our knowledge 
contain in them a distinct reference to the extent 
of the subject covered by such answers and state- 
ments, they are called determinate whether the 
whole or some definite part of the whole subject has 
been considered. 

We have seen that statements may be deter- 
minate or indeterminate in what they assert. Our 
thought, that is to say, may refer to a definitely 
specified area of a given subject, or it may refer to 
an indefinitely specified area. In the former case, 
the definitely specified area may be either the whole, 
or an indicated part of the whole. In the latter case, 
we cannot tell whether the knowledge expressed in 
the statement is true of the whole or of only a part 
of the whole. Now these distinctions in the ordinary 
use of language lie at the foundation of the logical 
consideration of propositions from the standpoint of 
quantity. Hence, the question of the quantity of 
propositions is whether what a statement connotes 



228 A TEXT-BOOK OF LOGIC 

is true of a specified or unspecified part of what its 
subject denotes. When, consequently, we speak 
about the quantity of a proposition, we must be 
understood to be interested in the meaning of a state- 
ment from the standpoint of the number of the ob- 
jects to which the statement applies. It is obvious 
that the subject terms of all propositions which ex- 
press quantity must be read in denotation. 

If now we ask, To how many objects can we in- 
tend our statements to apply? we may answer to 
one, to more than one but less than all, and to all. 
These are all the possible cases, and they afford a 
clue to the classification of propositions from the 
standpoint of quantity. 

The Singular Proposition. When a statement is 
made of one specified individual, that statement, in 
logic, is said to be a singular proposition. 'Hannibal 
was a great Carthagenian general' is, in this sense, 
a singular proposition. It is a proposition that ex- 
presses what an examination of a single instance of 
the genus 'general' has led us to affirm. This is not 
an exceptional case, for we are frequently led, in 
the course of our experience, to examine single ob- 
jects and to attempt some classification of them. 
The child's questions, 'What is this?' 'Who made 
that?' and the like are illustrations of the impor- 
tance of this class of judgments in the progress of 
intelligence and the advancement of knowledge. 
Singular statements are concrete, or keep us in close 
connection with what is concrete, and for this reason 
are of great help in making exact, particular, and 



CATEGORICAL PROPOSITIONS 229 

precise the knowledge that, in one way and another, 
we are daily acquiring. The examination of indi- 
vidual objects is, also, a large part of the work of 
any science, and much of the knowledge that science 
has consists of the singular judgments it is able to 
assert. We may say in passing that the student's 
danger is that he will get away from the observation 
of particular things, and that his education will 
force him to premature generalisation in which a 
form of words is substituted for a face to face 
acquaintance with the facts of his special subjects 
of study. If such should be the case, it is hardly 
possible that he will appreciate the importance of 
this type of proposition. 

The Universal Proposition. Another class of 
propositions is met with when the subject terms of 
such propositions are general instead of individual. 
'All democratic governments tend to issue in despot- 
ism' is a statement expressing a judgment that pur- 
ports to be based upon the common character of the 
individuals that the general term signifies. Greek, 
French, British, American, etc., are the governments 
of which such a statement is held to be true, and 
yet not as Greek, French, etc., but as democratic. 
Statements of this kind are made because there is 
conceived to be a necessary connection between what 
the predicate and subject terms connote, and they 
apply to all individual or particular instances which 
possess the attributes of the subject term. In other 
words, whenever we affirm or deny of each of a total 
number of instances the meaning that attaches to 



230 A TEXT-BOOK OF LOGIC 

the predicate terms of propositions, we have what, 
in logic, is called a universal proposition. 

Kinds of Universal Proposition. A question may- 
arise as to whether there is any logical difference 
between a singular and a universal proposition, since 
in both cases, the subject term must be understood 
to be distributed, that is, to apply to the whole num- 
ber of the instances that the connotation of the term 
implies. There can be no objection to taking these 
two cases as illustrating the same logical principle, 
namely, that from the standpoint of their quantity 
we intend our statements to apply to all the in- 
stances, whether to a specified one or to all, to which, 
in the nature of the proposition, the subject term can 
apply. The singular proposition may thus be taken 
as a particular form of the universal proposition. 
Another type of proposition which, like the singular 
proposition, has a concrete subject term, and which, 
on account of the definiteness of its denotation, has 
to be interpreted as a universal proposition may be 
considered in this connection. For example, in the 
proposition, 'A part is always less than the whole/ 
a part is a perfectly determined idea of quantity 
from the logical point of view, and the proposition 
in which it serves as a subject term must, therefore, 
be treated as a universal proposition. 

The Particular Proposition. Whenever the num- 
ber of instances denoted by the subject term of a 
proposition is, from the logical standpoint, unde- 
termined, we are said to have a particular proposi- 
tion. The question for us to bear in mind in decid- 



CATEGORICAL PROPOSITIONS 231 

ing the quantity of a proposition is simply whether 
the number of instances of the kind connoted by the 
subject term is a determined number or not. For 
example, if we say that 'Five per cent of all college 
students fail in their work,' it is clearly not meant 
that we know the exact number of college students, 
and therefore that we know the exact number who 
fail ; the statement, if it is true, must be based upon 
the examination of large numbers of students work- 
ing under a great variety of conditions, and, when 
so based, we feel warranted in saying, even with 
respect to those students who have not had an oppor- 
tunity to pass or to fail in any subject, that in the 
period covered by their college course five per cent 
of these will fail. Now what we wish to illustrate 
by this example is that the statement is a universal 
one because, although arithmetically we have no 
idea of the number of failing students, we do have 
in the subject term of our proposition, 'five per cent 
of all college students,' an idea logically determined 
from the standpoint of its quantity. 'Five per cent' 
is just as definite as 'this one' of a given number, 
and both are as definite as 'all' of the given number. 
But if, on the contrary, in the absence of all knowl- 
edge of any such statistical study as we have sup- 
posed, we were required to express our judgment 
as to the number of failures likely to be incurred 
at any given time, we could not logically go beyond 
the statement that 'Some students will fail in their 
work.' This statement is true of an undetermined 
number of students, and 'some,' as a sign of quantity 



232 A TEXT-BOOK OF LOGIC 

in propositions, means this. The propositions that 
express judgments that have not determined the 
quantity of their subject-matter are called particular 
propositions. 

The Indesignate Proposition. Whenever we ex- 
press judgments of quantity, our statements, as a 
rule, bear upon their face some definite indication 
of the extent of their subject terms. From the 
standpoint of quantity, all our statements are offered 
as true of a number of determined or undetermined 
individuals, and when a statement is made without 
specifying which of these two possibilities is meant, 
we are left in doubt as to how the statement is to 
be taken. Now sometimes this occurs. The popular 
wisdom of an age which gets itself hardened into 
proverbs is frequently defective in this respect. 
'Dead men tell no tales,' is an illustration in point. 
Are we to understand this of all dead men or only 
of some dead men? Is there, that is, a necessary 
connection between being dead and being unable to 
appear as a witness in a trial, for example; or are 
we to suppose that there is only an accidental con- 
nection between them, and that in some cases the 
testimony of dead men is admissible? 'Virtue is to 
be rewarded,' is a proposition that is defective in 
the same respect. Are we to understand this of each 
and all the virtues, of the ordinary virtues of our 
daily life as well as of the more heroic virtues that 
are called out in exceptional circumstances; or are 
we to limit the statement to the latter class of casr° ? 
If the latter, then the same set of questions recurs, 



CATEGORICAL PROPOSITIONS 233 

and we should wish to know whether a reward must 
be attached to all of them or to only some of them. 
These illustrations are sufficient to indicate a kind 
of statement we sometimes meet with even in com- 
mon life, statements that are quantitative by impli- 
cation but are not explicitly so. How are we to 
deal with them logically? Our first inclination is to 
receive all such statements, according to the charac- 
ter of their subject-matter, as universal or par- 
ticular propositions. But if it is remembered that 
all propositions are expressions of the judgments of 
the person who states the proposition, and that they 
are, from the standpoint of the person who hears 
them, proposals for his acceptance or rejection in 
the sense in which they are made, it will be obvious 
that we are not allowed to interpret these statements 
in any sense we wish ; our business is to understand 
them in the sense they have for the person who 
makes them. But, as we saw, these propositions 
create a doubt that is based upon the possibility of 
understanding the statements in either of two ways. 
Whenever a statement raises a doubt of this kind, 
a doubt that may be resolved by accepting either 
the one or the other of alternative possibilities, 
without indicating which alternative is to be 
adopted, it is called an indesignate proposition. An 
indesignate, or as it is sometimes called, an indefinite 
proposition is one which implies the existence of a 
determined or undetermined number of individuals 
of which the statement is offered as true, but which 
fails to state explicitly whether it is made of the 



234 A TEXT-BOOK OF LOGIC 

number of the determined or of the undetermined 
instances. 

Quality of Propositions. Our study in a previous 
chapter has shown that terms always intend more 
than they express, that they are aspects of a whole 
meaning which as terms they do not fully bring out. 
We have also learned that in order to get at the 
full meaning of any term we must find it functioning 
in some way in a proposition. It is only in a prop- 
osition that we discover the full meaning of a term ; 
the proposition is the express statement of the whole 
meaning within which the meanings of terms may 
properly be sought. In other words, it is the way 
that terms function in propositions that gives the 
key to the meaning of the proposition and of the 
terms themselves. That is to say, we have to inter- 
pret terms from the standpoint of their propositions 
and proposition from the standpoint of their terms. 
The reason is that each implies the other, and 
neither can exist alone. 

Coming now to the particular problem of this 
section, we may see, in the light of what has just 
been said, that terms may be related to one another 
in propositions in one or the other of two ways, in 
the way of inclusion or of exclusion. The fact that 
terms are elements of the meaning expressed by the 
proposition, is indicated, as we have already seen, 
by the copula. The copula, we said, is the sign of 
predication, the sign that S and P are to be taken 
in the way required by the whole meaning expressed 
in the proposition. One of the ways in which prop- 



CATEGORICAL PROPOSITIONS 235 

ositions require us to take their terms is, as we said, 
with respect to whether they are inclusive or exclu- 
sive of each other. And this requirement is indi- 
cated by the copula, which according as it has or 
has not the negative particle 'not,' distinguishes for 
us the two kinds of Quality of propositional state- 
ments. When the terms are inclusive, this is indi- 
cated by the copula 'is' or 'are;' when they are ex- 
clusive, by the copula 'is not' or 'are not.' The 
propositions that have respectively these two kinds 
of copula are called affirmative and negative prop- 
ositions. Affirmative and negative propositions, 
therefore, are statements that give expression to 
the inclusive and exclusive relationship of the terms 
through which our meanings are expressed. 

The Affirmative Proposition. Affirmative propo- 
sitions, formally considered, are those in which the 
copula is either 'is' or 'are.' From the standpoint 
of the character of the thought expressed in them, 
affirmative propositions may be defined as the ex- 
pression of our positive meanings. By a positive 
meaning we understand one which combines in a 
whole content of thought two or more features of 
the object thought about. Stated differently, a pos- 
itive meaning is one that may be analysed into ele- 
ments each of which expresses some feature of the 
meaning which the proposition as a whole expresses. 
For example, the meaning of the proposition, 'All 
mammals are vertebrates' is, that there is a genus 
which, when looked at from the standpoint of an- 
atomy, must be described as a vertebrate, but which 



236 A TEXT-BOOK OP LOGIC 

if looked at from the standpoint of physiology must 
be described as a mammal. Let us call the genus, 
or the whole meaning of any proposition, SP. Then 
our positive meaning, SP, may be analysed into S 
and P, and these terms may be used to express the 
intended meaning in the proposition 'S is P.' To 
develop the significance of affirmative predication 
further, we may say that in any statement of the 
form 'S is P,' S and P are not isolated or independent 
terms ; S is not merely S, nor is P merely P. What 
the proposition affirms is that the S that is P is an 
SP, and only because it is SP can we say that it is 
P. But P can be predicated of S only if it also is 
SP. SP underlies both terms, and gives to the mean- 
ing that the proposition 'S is P' expresses its posi- 
tive character. 

The Negative Proposition. Negative proposi- 
tions, formally considered, are those in which the 
copula is either 'is not' or 'are not.' Materially, that 
is, from the standpoint of the character of the 
thought expressed in them, negative propositions 
may be defined as the expression of our exclusive 
meanings. By a negative meaning, therefore, we 
understand one which excludes from a whole con- 
tent of thought one or more attributes of the object 
thought about, either because it does not at all, or 
because it does not now, form part of the connotation 
of the whole content of thought. Stated otherwise, a 
negative meaning is one which may be analysed into 
elements one or more of which is incompatible with 
some fact or truth which we have already accepted. 



CATEGORICAL PROPOSITIONS 237 

In the chapter on terms we discussed negative 
meaning, and the conditions under which such mean- 
ings arise were explained. These conditions can be 
reviewed profitably in the present connection, and 
they will be found to throw light upon the general 
statement in the present parapragh of what we 
understand a negative meaning to be. 

We shall pass on to other aspects of the same 
problem. We may call attention then to the fact 
that the predicate terms of negative propositions 
are to be read in connotation. The reason for this 
is that logical negation expresses incompatibility in 
the meanings of terms. For example, 'Apples are- 
not pears/ does not express merely the perceptual 
differences of the things we call apples and the things 
we call pears ; what the proposition means is that if 
we know what attributes pears have, they will be 
found not to be the attributes which apples have. 
Now, as we see by this illustration, the difficulty 
about negative statements is that they seem to break 
the connection that, as we said, must bind S and P 
together in logical propositions. For example, we 
have shown that, in order to make any statement of 
the kind S-P, we have to suppose that P is predi- 
cated of S on the ground of the common likeness that 
underlies the differences of S and P. It is, in other 
words, because S and P make a reference to the same 
subject, although to different aspects of it, that pred- 
ication can take place at all. Can we say that in neg- 
ative propositions there is the same identity in dif- 
ference that is the ground of every logical state- 



238 A TEXT-BOOK OF LOGIC 

ment? It would seem that we can; only the differ- 
ences, in this case, have come in our thought to be a 
special motive for the judgment we assert. In other 
words, in affirmative propositions we express like- 
nesses amid differences, while in negative proposi- 
tions we express differences amid likenesses. The 
negative proposition has this characteristic because, 
by making difference the motive of our assertions, 
we can sometimes best conserve the unity of idea 
that every propositional statement requires. 

The Relation of Affirmative and Negative Prop- 
ositions. A study of the relation of affirmative and 
negative statements will throw still further light 
upon the meaning of negation. In affirmative state- 
ments, thought moves between two extremes, the 
extreme of tautology on the one hand, and the ex- 
treme of nonsense on the other. If we take affirma- 
tion in one extreme way, we can only express iden- 
tical meanings, 'A boy is a boy/ and this is taut- 
ology. If we take affirmation in another extreme 
way, we can only express incompatible meanings, 
'A stove is a gold mine,' and this is nonsense. Now 
it is the function of negation to save us from mean- 
ingless — tautological or nonsensical — assertions. 
For instance, the case of tautology, when taken 
absolutely, is a denial of the minimum of difference 
which must exist if we are to make our assertions 
significant. Merely to predicate an object's exist- 
ence of itself, or to affirm a meaning of itself, is 
nothing but trifling. If we should mean by the 



CATEGORICAL PROPOSITIONS 239 

predicate only what we mean by the subject of a 
proposition, we should state in the whole proposi- 
tion no more than we stated in either of its terms. 
Thus, 'A is A' has exactly the meaning of A, whether 
A is read denotatively in both terms, or connota- 
tively in both terms. If A is A is a significant state- 
ment, we must at least read A denotatively in one 
term, and connotatively in the other. In other 
words, the identity which unites the subject and 
predicate of logical propositions must not go to the 
extreme of eliminating all differences from the 
meaning which logical propositions state. The 
affirmative proposition, because its chief interest 
is in identity, is particularly open to the danger of 
overlooking the differences that make the subject 
and predicate of such propositions distinct terms. 
Now, when this happens, when identity usurps the 
whole functions of assertion, we can be saved from 
the fatuity of tautology by resorting to negation as 
the only means at our disposal for opening the way 
to some significant statement. Thus, if we oppose 
any tautology with a denial, the burden of the proof 
of what we assert is thrust upon us, and this con- 
sists in showing the grounds on which our negation 
rests. For example, if we deny that 'A boy is a boy,' 
we may do so because, as we may point out, he is 
also a son, and that this relationship is compatible 
with the fact of boyhood from which, in the tauto- 
logical statement, we were unable to get away. 
Negation serves, in such a case, to prevent us from 



240 A TEXT-BOOK OF LOGIC 

standing intellectually stock-still; and, as we often 
find, the denial of truism may sometimes be the 
open way to the truth. 

The other extreme to which affirmative judg- 
ments may lead us consists in the development of 
differences to such an extent that the unity of the 
judgment is threatened or completely destroyed. 
This may occur, for example, when the material of 
the judgment is forced to render so many predicates 
that the universe of discourse, which in all logical 
judgment sets the limit to which differences can be 
carried, is in danger of being superseded, and the 
qualities which the material may have in other uni- 
verses of discourse are brought in to satisfy the 
demand for differences which has, so to say, got out 
of hand. When, for example, the student of psy- 
chology speaks of auditory sensations being brought 
in over the auditory nerve, and when the text-books 
of physiology speak about the striated muscles being 
under the control of the will, there is a confusion 
of universes of discourse, and we can only force the 
statements within their respective bounds again by 
a refusal to accept them as significant assertions. 
The statements are incompatible with the body of 
knowledge of their respective sciences, and the nega- 
tion is in each case in the interests of this body of 
accepted knowledge. 

Exceptive and Exclusive Propositions. Whenever 
a subject of discourse is qualified by such words as 
except, only, but, unless, alone, none but, etc., it 
immediately becomes uncertain to what, in such 



CATEGORICAL PROPOSITIONS 241 

cases, the predicate applies. For example, if we say, 
'All free persons know how to obey/ it is quite ob- 
vious that we are predicating 'the knowledge of how 
to obey' of 'the persons who are free.' If, however, 
we were to say 'None but the free know how to obey,' 
we should be saying something quite different, al- 
though most persons would understand that we were 
still predicating 'the knowledge of how to obey' of 
'the persons who are free.' If, again, we said, 'Only 
the free know how to obey,' it might be asked 
whether we had said something identical with one of 
the other statements, or something different from 
both. And, further, if we said, 'No one unless he is 
free knows how to obey,' the problem would become 
still more complicated. 

In view of the difficulties of interpretation occa- 
sioned by such statements as those to which atten- 
tion has just been called, it is customary for logic 
to point out that all propositions whose subject 
terms are qualified by such words as except, only, 
but, are either exceptive or exclusive propositions. 
In the exceptive and the exclusive proposition the 
subject term is an infinite or non-S term, because all 
the qualifying words, except, but, only, etc., are 
understood as carrying a negative signification. 
Examples are : 'All except honor' = 'All that is not 
honour ;' 'None but the free' = 'No one who is not 
free;' 'Only natives' = 'No one who is not a native.' 
It should be observed, moreover, that exceptive and 
exclusive propositions are always universal, there 
are no particular propositions of either kind. That 

16 



242 A TEXT-BOOK OF LOGIC 

is to say, the subject terms of these propositions 
denote always a determinate number of individuals. 
But while the exceptive and exclusive propositions 
distribute their non-S terms, they differ from each 
other in quality. That is to say, all propositions 
which qualify their subjects in the manner indicated 
are either affirmative or negative. In the light of 
these statements we may consider these classes of 
propositions separately. 

The exceptive proposition is affirmative. It ha& 

the general form, SaP. Examples are : 'All planets 
except Venus and Mercury are beyond the earth's 
orbit' = 'Any planet that is not Venus or Mercury 
is beyond the earth's orbit;' 'All members but the 
Irish voted for the measure' = 'All the members 
who do not belong to the Irish party voted for the 
measure.' 

In an exceptive proposition the individuals de- 
noted by the subject term are determined by taking 
out of a class a certain number of individuals to 
which the predicate term is meant not to apply. It 
will be seen that if the part of the class to which 
the predicate term does apply is to be distributed, 
the part taken out must be distributed also. What 
an exceptive proposition says, therefore, is that a 
statement is true of that part of a class which re- 
mains when stated exceptions to it are definitely re- 
moved. The truth of such a statement is maintained 
of everything that cannot be brought under the ex- 
ception, that is, of everything that is not the speci- 
fied exception. Consequently, what we are talking 



CATEGORICAL PROPOSITIONS 243 

about, in an exceptive proposition, is anything, 
within the universe of discourse, that is definitely 
non-S. Thus, if a circle represents a universe of 
discourse, and any shaded portion of it the excepted 
part, which may be called S, the unshaded part will 
then represent the denotation of the subject of 
predication, that is, non-S. The exceptive proposi- 
tion may in these terms be represented thus : 




SaP 

The exclusive proposition is negative. It has the 
general form, SeP. Examples are: 'None but the 
brave deserve the fair' = 'No one who is not brave 
deserves the fair;' 'Only graduates are eligible' = 
'No one who is not a graduate is eligible.' 

The exclusive proposition determines its subject 
term in the same way as the exceptive proposition, 
that is, by taking out of a class some determinate 
number of individuals, and making all other indi- 
viduals of the class the subject of predication. Thus, 
if S be the excluded individuals, non-S will be the 
subject of which predication takes place. But since 
exclusive propositions are negative, the individuals 
denoted by non-S will necessarily have qualities 
which are incompatible with their possessing those 
connoted by the predicate term; incompatibility of 
qualities is what we mean by negation. Hence, the 



244 A TEXT-BOOK OF LOGIC 

exclusive proposition definitely denies P of every 
individual which does not have the qualities also of 
S ; nothing that is not S is P. If, now, we represent 
any excluded part of a class by the shaded portion 
of a circle, the exclusive proposition may be shown 
as follows: 




SeP 

Compound Propositions. We have said that ex- 
ceptive and exclusive propositions are always uni- 
versal. This is not because particular propositions 
do not qualify their subject terms by such words as 
only, except, etc., but because when they do, they 
must be treated as compound propositions. By a 
compound proposition, or, as the older logicians 
called them, exponible propositions, is understood 
one whose meaning requires a number of distinct 
propositions for its complete expression. 'Milton 
and Dante wrote religious poetry of the highest 
merit/ is a simple example. The meaning of the 
statement obviously is, (a) 'Milton wrote religious 
poetry of the highest merit,' and (b) 'Dante wrote 
religious poetry of the highest merit.' A more com- 
plex example is, 'Men who are honest though poor 
will be respected and helped.' The whole sense of 
this can be expressed in the two statements (a) 
'Poor men who are honest will be respected,' and 
(b) 'Poor men who are honest will be helped.' From 



CATEGORICAL PROPOSITIONS 245 

these examples we can see that a separate expres- 
sion must be given to each significant idea of any- 
complex of ideas. 

Bearing in mind what a compound proposition 
is, let us turn to the particular propositions which 
qualify their subject terms by the use of exclusive 
words or phrases. These propositions, we have said, 
are compound. An example is, 'Some only who en- 
list will find their way to the firing line.' This 
obviously cannot mean, 'Some who do not enlist will 
find their way to the firing line;' that is, it cannot 
be treated as a particular exclusive proposition. 
What the statement means is (a) 'Some who enlist 
will find their way to the firing line,' and (b) 'Some 
who enlist will not find their way to the firing line.' 
The following must also be treated as a compound 
proposition, 'Excepting a few, all these answers are 
wrong.' What the proposition states is (a) 'Some 
of these answers are wrong,' and (b) 'Some of these 
answers are not wrong.' From these examples it 
seems obvious that whenever we qualify, in the way 
indicated, the subject terms of particular proposi- 
tions, that is, whenever 'some' is used in its exclusive 
sense, the proposition must be resolved into two 
independent particular propositions, the one affirm- 
ative and the other negative. In the light of these 
cases, we may also understand why the particular 
proposition which has no such exclusive significance 
must be interpreted as either affirmative or nega- 
tive, and not as both. For instance, 'Not all for- 
eigners are to be mistrusted' means 'Some foreigners 



246 A TEXT-BOOK OF LOGIC 

are not to be mistrusted;' and if any one were to 
add to this interpretation, 'Some foreigners are to 
be mistrusted,' he would be going beyond what is 
said to a secondary implication of what is said. The 
latter statement is doubtless implied in the original 
statement, but it is not what that statement asserts. 
Modality of Propositions. The knowledge we 
have of different subjects, as we are all aware, varies 
not only with respect to the nature of these subjects 
themselves, so that one kind of knowledge we call 
history, and another science, and another phil- 
osophy, but also with respect to the degrees of our 
attainments in any of these departments of knowl- 
edge, so that we speak about these several subjects 
with differing degrees of confidence. If, for ex- 
ample, the student has diligently pursued the study 
of bacteriology for a number of years he will not 
only know a great deal about the nature and condi- 
tions of the changes that microscopic organisms 
produce in their hosts, but he will have developed, 
with his increasing knowledge of the subject, a cer- 
tain degree of confidence in his ability to describe 
these changes, to prepare cultures, and to do many 
things besides. If the same student has not given 
a good deal of time to the study of history, he will 
not feel the same degree of confidence that we ob- 
served in the former case, if he were asked to name, 
for instance, the causes that produced the French 
Revolution. There are, then, different degrees of 
knowledge, and these get reflected in the degrees of 
confidence with which we express what we know. It 



CATEGORICAL PROPOSITIONS 247 

is this fact that logic refers to under the term Mo- 
dality. The meaning of this statement may become 
clearer if it is pointed out that the term modality 
does not refer to any uncertainty that may exist 
as to the nature and relations of the object of judg- 
ment, but only to the degrees of certainty of our 
knowledge of the object. Modality, that is to say, is 
a logical distinction; it characterises our thoughts 
about things, and not the things themselves. Whether 
there is any uncertainty in things themselves can- 
not be discussed in an elementary logic, but that 
varying degrees of certainty and uncertainty attach 
to our knowledge of things is a fact well known to 
all. 

It is usual, in logic, to distinguish three degrees 
of certainty, and to throw these into typical proposi- 
tional forms when we wish to express the modality 
of our thought. The propositions which set forth 
the modality of our judgments are called assertoric, 
problematic and apodeictic. We may state what is 
to be understood by each of these in order. 

The Assertoric Proposition. An assertoric prop- 
osition has the same form as the affirmative cate- 
gorical proposition, and yet is not to be understood 
in the same way. The categorical proposition ex- 
presses the way that S and P are related in the uni- 
verse of discourse that defines the limits of the judg- 
ing activity, and, therefore, relates to the matter of 
the judgment. The assertoric judgment, on the 
other hand, expresses one of the degrees of certainty 
of our knowledge about the subject-matter. For 



248 A TEXT-BOOK OF LOGIC 

example, if we were to say, 'All men are biped/ we 
should most likely be understood to express a judg- 
ment founded upon common observation, and that 
is what the categorical proposition of the form, 
'S is P,' usually does. If, however, with respect to 
this judgment, we were asked, 'What makes you 
think so?' we should possibly hunt around the var- 
ious corners of our knowledge for a reason for think- 
ing that walking on two feet is characteristic of all 
men. If from such an excursion and search we 
were to return without anything that threw light 
upon the question, we should probably reply, 'I don't 
know, but he is a biped.' We should, that is, assert 
with emphasis our original statement, and thereby 
express our confidence in the correctness of the 
original statement. What, therefore, an assertoric 
proposition does is to assert that S is actually P, or, 
stated another way, that 'S is P' is actual, whether 
any reason, other than perception or memory sup- 
plies, can be given or not. 

The Problematic Proposition. A problematic 
proposition states that 'S is possibly P,' or the fact 
expressed by *S is P' is possible. The possibility 
does not imply any uncertainty in the fact expressed, 
but only an uncertainty in the state of our knowl- 
edge about the fact, an uncertainty that makes it 
impossible for us to state with any higher degree 
of confidence the correctness of what we say. For 
example, the student who is reading this section of 
logic may say, 'My understanding of the subject is 
possibly correct.' What he means by this is not 



CATEGORICAL PROPOSITIONS 249 

that his understanding may be described as possibly 
correct, for there is no such thing as 'possibly cor- 
rect,' but that the statement, 'My understanding of 
this subject is correct' is a possibility in his own 
case. If we take a simpler case this will become 
clear. The rose is possibly white' does not mean 
that 'possibly white' is the colour that the rose has, 
for there is no such colour. We are to understand 
the adverb to qualify not any part of the statement, 
but the whole assertion — 'The rose is white,' and 
then, as in the other case, this statement expresses 
a possibility. 

If this is the view that we must adopt of prob- 
lematic propositions, what, we may ask, is the 
ground of the implied uncertainty? The uncertainty 
is not due, as in assertoric propositions, to the fact 
that there are no discoverable reasons for the state- 
ment, but that the discovered grounds of the state- 
ment are of such a nature that we can never be sure 
that we have all the elements necessary to give our 
statement any higher degree of certainty. To illus- 
trate : the student's understanding of this paragraph 
must, as we know, be correct or incorrect, just as the 
rose must have any one or other of the colours that 
belong to the species rose. If we have not seen the 
rose in question, we know only that it is either red 
or pink or white or yellow, and because it may be 
something else than what we assert, we merely say 
that it is possibly white. So in the case of the stu- 
dent: his understanding is either correct or incor- 
rect, but because the alternatives have not been de- 



250 A TEXT-BOOK OF LOGIC 

termined with respect to the case in hand, he can 
only say that his understanding of the paragraph 
is possibly correct. A possibility, therefore, means 
the presence of alternatives between which no 
ground of decision has as yet been found. 

Judgments which involve human volition as one 
of their factors, even when these judgments involve 
no alternatives, are said to be problematic. For 
example, 'I may go tomorrow,' means that 'I will 
go tomorrow' is the statement of a fact that is pos- 
sible. Here we have not a series of alternatives as 
the ground of the uncertainty of the judgment, but 
the absence of some of the factors that are neces- 
sary for a more positive statement. All actions that 
depend on human volition are said to be contingent, 
and therefore a judgment that involves volition as 
one of its factors must always be problematic. 

The Apodeictic Proposition. Apodeictic judg- 
ments are necessary: 'S must be P.' There exists, 
in this case, necessary grounds for the matter of 
fact judged. 'S is P' is necessary. Necessity is a 
word that must be used carefully. This is obvious 
if we call attention to the different kinds of neces- 
sity upon which our apodeictic statements depend. 
Mathematical statements, although not expressed in 
the form of apodeictic propositions, are necessary. 
For example, 'A straight line is the shortest dis- 
tance between two points.' What the mathematician 
understands by this statement is that the shortest 
distance between two points must be what we mean 
by a straight line. The idea of a straight line 



CATEGORICAL PROPOSITIONS 251 

carries that meaning necessarily. Here, then, we 
have necessity resting upon the clearness with 
which an idea itself is conceived or apprehended, 
and not on anything else. Another class of neces- 
sity is met with when our judgments rest upon 
other judgments which may or may not be neces- 
sary. For example, the equality of triangles on 
equal bases and between the same parallels is a 
case of necessity resting upon grounds that are 
themselves necessary. In all truly apodeictic judg- 
ments there is presumed to be an inter-connection 
of fact that makes the fact asserted by the judg- 
ment necessary. 

REFERENCES 

B. Bosanquet, The Essentials of Logic, Lect. VII. 

J. G. Hibben, Logic, Deductive and Inductive, Chs. VII., VIII. 
W. S. Jevons, Lessons in Logic, Lesson VIII. 
J. N. Keynes, Formal Logic, 2d Edition, Part II., Ch. I. 
S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
tion, Ch. III., Part I. 

C. Read, Logic, Deductive and Inductive, 3d Edition, Ch. V. 

ADVANCED 

J. M. Baldwin, Thought and Things, Vol. II., Part II., Ch. 

VIII. 
B. Bosanquet, Logic, Vol. I., Book L, Chs. II-IX. 
F. H. Bradley, The Principles of Logic, Book I., Chs. VI- 

VIII. 
R. W. B. Gibson, The Problem of Logic, Ch. VII. 
H. W. B. Joseph, An Introduction to Logic, Ch. VIII. 
H. Lotze, Logic, Vol. I., Ch., II. 
J. S. Mill, A System of Logic, Book I., Ch. IV. 
F. C. S. Schiller, Formal Logic, Ch. XI. 



252 A TEXT-BOOK OF LOGIC 

C. Sigwart, Logic, Chs. IV-VI. 

J. Welton, A Manual of Logic, Book II., Ch. I. 

QUESTIONS 

1. What is the ground of the difference between the three 
types of propositions? 

2. Describe the four main classes of categorical proposi- 
tions. 

3. Explain and illustrate what you understand by the 
quantity of propositions. 

4. What is a singular proposition? Illustrate and state 
its importance. 

5. What is a universal proposition? 

6. What is the relation of the singular and universal prop- 
osition? 

7. What is a particular proposition, and with what form 
of universal proposition is it most likely to be confused? 

8. Describe and illustrate the indesignate proposition. 

9. What do you understand by the quality of propositions? 

10. What are the characteristics of affirmative propositions? 

11. Describe and illustrate a negative proposition. 

12. Why must the predicate of negative propositions be read 
connotatively? 

13. What is the relation of tautology to affirmative state- 
ments? 

14. In what way can tautological statements be overcome? 

15. What is the logical status of nonsense? 

16. In what respects are exceptive and exclusive proposi- 
tions alike? 

17. State and illustrate the characteristics of exceptive 
propositions. 

18. What is an exclusive proposition? Illustrate. 

19. Why are there no particular exceptive or exclusive 
propositions ? 

20. What is a compound proposition? By what other name 
is it known? Illustrate. 

21. Explain what is meant by the modality of propositions. 



CATEGORICAL PROPOSITIONS 253 

22. What is an assertoric proposition, and how does it 
differ from the categorical proposition? 

23. Explain and illustrate the problematic proposition. 

24. How will you classify judgments which involve human 
volition as one of its factors? 

25. Describe and illustrate the apodeictic proposition. 

EXERCISES. 

1. Write in parallel columns a list of six singular and six 
general propositions, and be ready to defend the as- 
signed character of these propositions. 

2. What kind of proposition is, 'Water is a liquid composed 
of one part oxygen and two parts hydrogen.' Give rea- 
sons for your answer. 

3. What is the distribution of the predicate term of the 
proposition in the preceding question? 

4. Give three illustrations of indesignate propositions. 

5. What kind of proposition is, 'Oxygen is necessary for 
the maintenance of life'? 

6. Without using the sign of quantity 'some/ give three 
illustrations of particular propositions. 

7. Classify the following propositions from the standpoint 
of quantity, and in each case state the reason for your 
classification : 

(1) Each of the hunters shot a bird. 

(2) Rivers generally run into the sea. 

(3) Blood is thicker than water. 

(4) Afflictions are often salutary. 

(5) Can the leopard change his spots? 

(6) Veteran soldiers are the steadiest in battle. 

(7) Suspicion ever haunts the guilty mind. 

(8) Knowledge is power. 

(9) The longest road has an end. 

(10) Almost any Turk hates a Greek. 

(11) Philosophy and Psychology are necesary to a well- 
rounded education. 

(12) Only those who know are in the end to be trusted. 



254 A TEXT-BOOK OF LOGIC 

8. Illustrate how affirmative statements can be made either 
tautological or nonsensical. 

9. Write a complete account of how one negative state- 
ment of your own selection may conceivably have come 
to be made. 

10. Write a list of three assertoric propositions, and show 
how they differ from affirmative categorical proposi- 
tions. 

11. Explain the problematic nature of six propositions of 
your own selection. 

12. Write a list of three apodeictic propositions. 



CHAPTER IX 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 

Relation of Quantity and Quality in Categorical 
Propositions. When the subject term of a proposi- 
tion is read in denotation, it refers to a determined 
or undetermined number of individuals, and when 
the predicate term of a proposition is read in conno- 
tation, it either affirms or denies the meaning of the 
predicate term of the individuals denoted by the 
subject term. Now, since every proposition under- 
takes to set forth both these relations of its subject- 
matter, there are no propositions which do not pos- 
sess both quantity and quality. 

From the standpoint of their quantity, categor- 
ical propositions, as we have seen, are either univer- 
sal or particular; that is, logical statements are 
always about a determinate or indeterminate part 
of the subject-matter of such statements. From the 
standpoint of their quality, categorical propositions 
are either affirmative or negative; that is, logical 
statements either affirm or deny an attribute of 
some determinate or indeterminate part of their 
subject. Combined in a single statement, these 
facts and relations may be expressed thus : Propo- 
sitions with distributed, as also those with undis- 
tributed, subject terms are either affirmative or 
negative in quality. There are thus four proposi- 
tions, — the universal affirmative, the universal neg- 

(255) 



256 A TEXT-BOOK OF LOGIC 

ative, the particular affirmative, the particular neg- 
ative, — whose relations may be shown in a table 
as follows: 

QUANTIT\ QUALITY 

f a. Affirmative 
'Universal J 

b. Negative 



Propositions - 



f a. Affirmative 
Particular J 

I b. Negative 



This table may be read: Propositions may be 
universal in quantity and either affirmative or neg- 
ative in quality ; or they may be particular in quan- 
tity and either affirmative or negative in quality. 

Structural Formulae indicating the Quantity and 
Quality of Propositions. The problems that we are 
to study in this chapter arise out of the fact that 
propositions involve the relations both of quantity 
and quality. Whatever else the student can or can- 
not do with a proposition, it is of fundamental im- 
portance that he should be able to determine it both 
with respect to its quantity, and also with respect to 
its quality. The student will find it entirely possible 
to acquire a considerable degree of facility in thus 
determining the propositions that come before him 
for study ; and, moreover, a little additional industry 
in this matter will carry him a long way toward 
overcoming some of the difficulties that he will meet 
farther along the road. When he has become prac- 
tically familiar with these distinctions, it will be a 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 257 

great convenience if, for the propositions that em- 
body these distinctions, he write formulae which 
indicate their quantity and quality. The value of 
such formulae is that they enable one to deal only 
with the essential aspects of assertions, and they 
shorten the method of referring to these essential 
aspects. Like any other formulae, those used in 
logic are more or less arbitrary devices, and are to 
be justified by their usefulness. They are in no 
sense a substitute for the logical facts and relations 
which they are merely the means of expressing. 

Our first aim then will be to distinguish by a 
convenient symbol the four typical propositions 
mentioned above. This is usually done by taking 
the first vowel of the Latin word for affirmation 
(affirmo) , and the first vowel of the Latin word 
for negation (nego) to denote the universal propo- 
sition of the quality indicated by the word, and the 
second vowel of each word in like manner to indi- 
cate the respective particular propositions. Thus, 
A and E, the first vowels in the words affirmo and 
nego, are used to indicate the universal affirmative 
and universal negative propositions respectively. 
The second vowels in the same Latin words are I 
and 0, and these are used to indicate respectively 
the particular affirmative and particular negative 
propositions. If, now, we add these facts to the 
table printed above, we have the following result : 



17 



258 



A TEXT-BOOK OF LOGIC 



Propositions 



QUANTITY 

1. Universal 

2. Particular 



QUALITY SYMBOL 

a. Affirmative A 

b. Negative E 

a. Affirmative I 

b. Negative O 



Whenever, in the foregoing pages, we have had 
occasion to refer to the structure of a proposition 
without respect to its quantity, we have written 'S 
is P,' or 'S is-not P.' Whenever we have wished to 
indicate the quantity as well as the quality of prop- 
ositions, we have written 'All S is P,' 'No S is P,' 
'Some S is P,' 'Some S is-not P.' This, however, is 
too cumbersome a method when a simpler one is 
possible. And, therefore, logicians have adopted 
the device of substituting for the copula in proposi- 
tions of the general form S-P, one or other of the 
four vowels by which the four kinds of categorical 
propositions are distinguished. In this way we get 
the following structural formulae: SaP, SeP, SiP, 
SoP, which are read 'All S is P,' 'No S is P,' 'Some 
S is P,' 'Some S is-not P.' 

The following table summarises the important 
facts : 

QUANTITY AND STRUCTURAL 

QUALITY FORMULA READ 

f 1. Universal Affirmative SaP All S is P 
2. Universal Negative SeP No S is P 



Propositions 



3. Particulare Affirmative SoP Some S is P 

4. Particular Affirmative SiP Some S is P 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 259 

This table should be read : Propositions as to their 
quantity and quality may be either universal affirm- 
ative, with the structural formula SaP which 
is read 'All S is P;' or universal negative, with 
the structural formula SeP which is read 'No S is 
P;' or particular affirmative, with the structural 
formula SiP which is read 'Some S is P;' or par- 
ticular negative with the structural formula SoP 
which is read 'Some S is-not P.' 

Distribution of the Terms of the Four Categorical 
Propositions. The logical meaning of distribution has 
been discussed in the chapter on terms, and we met 
the same question again when considering the quan- 
tity of propositions. We need, therefore, only repeat 
what was shown more at length above, that by dis- 
tribution is meant the width or extent of the mean- 
ing expressed in a proposition. We have seen, for 
example, that from the standpoint of quantity the 
subject terms of universal propositions are dis- 
tributed ; they denote a determinate number of indi- 
viduals, each of which possesses, or does not possess, 
in addition to the qualities connoted by the term 
itself, those qualities also that are connoted by the 
predicate term of such propositions. From the same 
standpoint, the subject terms of particular proposi- 
tions, on the other hand, are undistributed; they 
refer to an indeterminate number of denoted indi- 
viduals. 

We have now to ask what influence the quality 
of propositions has upon the distribution of pred- 
icate terms. And first let us consider affirmative 



260 A TEXT-BOOK OF LOGIC 

propositions. In affirmative propositions we pred- 
icate the attribute connoted by P of the object or 
objects denoted by S. So far as they are affirmative, 
propositions do not enable us to say whether there 
are any objects, other than those denoted by the 
subject term, to which the attributes of the pred- 
icate term apply. Sometimes there are such objects ; 
as, for example, The cat is a domesticated animal/ 
for, as we know, there are other domesticated ani- 
mals than cats. Sometimes there are not, as, for 
example, 'Perception is the consciousness of par- 
ticular material objects present to sense/ for there 
are no other objects to which such a description can 
apply except perception. In view of these facts, it 
is obvious that, from the form of the proposition, it 
is quite impossible to determine whether universal 
affirmative statements are to be understood in the 
one or the other of the ways just indicated; whether, 
that is to say, they may be said to have distributed 
or undistributed predicate terms. On account of 
this uncertainty, it is customary, in the absence of 
any reason connected with the subject matter to the 
contrary, to regard the predicate terms of such 
propositions as undistributed. 

The predicate terms of negative propositions, on 
the other hand, are distributed. The reason for this 
is that it is only when every object which can be 
included in the denotation of the predicate term is 
excluded from the subject that the proposition can 
have a negative force at all. For if all P's were 
not definitely separated from the S, some P's might 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 261 

be included in it, and this would not express the 
meaning of negation. Negation, as we have seen, 
has always a definitely exclusive force. And this is 
true of negative propositions irrespective of their 
quantity ; it is true of the particular as well as of the 
universal negative proposition. Of the universal 
proposition, SeP, this is easily seen to hold. For 
if 'No S's are PV has any meaning at all, it must 
surely mean that not any of the S's are any of the 
P's. That is to say, of none of the objects that have 
the qualities connoted by S can we affirm that they 
have also the qualities connoted by P. If that is 
true, no P's are any of the S's. But the same thing 
can be shown also of the particular proposition, SoP. 
'Some S's are-not P's' must mean that none of the 
objects denoted by S has the qualities connoted by 
P ; and that is equivalent to saying that none of these 
S's are at the same time P's. The objects denoted 
by P, if there are any, are entirely excluded from 
the number of objects referred to by S. If, in this 
case, any difficulty arises on account of the un- 
distributed nature of the subject term, we can only 
say that the meaning of the proposition is that there 
are at least some unspecified instances of S's that do 
not have the characteristics of P; and that if, as 
may or may not happen, you discover any S's that 
do have these characteristics, then they are not the 
S's to which the proposition refers. It follows, 
from these considerations, that the predicate terms 
of all negative propositions are distributed. 



262 



A TEXT-BOOK OF LOGIC 



We may summarise the foregoing discussion in 
the four following statements: 

1. The subject terms of propositions that are 
universal in quantity are distributed. 

2. The subject terms of propositions that are 
particular in quantity are undistributed. 

3. The predicate terms of propositions that are 
affirmative in quality are undistributed. 

4. The predicate terms of propositions that are 
negative in quality are distributed. 

Thorough familiarity with the distribution of 
the terms of categorical propositions is so essential 
to the student's understanding of what follows that 
he is urged to master the subject at this point of his 
studies. Because of the importance of the subject, 
and as a further aid to its mastery, we add the fol- 
lowing tables each of which represents the facts 
contained in the foregoing summary. The letters 
D and U stand for distributed and undistributed 
respectively : 

PROPOSITION 



STANDPOINT 


r 
SUBJECT 




PREDICATE 


STANDPOINT 




D 


a 


u 






D 


e 


D 




Quantity < 


u 


i 


U 


Quality 




u 





D 





This table may be read as follows : From the stand- 
point of quantity, the subject term of an A or uni- 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 263 

versal affirmative proposition is distributed; from 
the standpoint of quality, the predicate term of an 
A or universal affirmative proposition is undistrib- 
uted, etc. 

Another way of stating the same set of facts is 
to say that the subject terms of propositions that 
are universal in quantity are distributed, and those 
that are particular in quantity are undistributed; 
that the predicate terms of propositions that are 
affirmative in quality are undistributed, and those 
that are negative in quality are distributed. The 
following table represents these facts : 



Subject terms 



Predicate terms 



QUANTITY DISTRIBUTION 

(Universal D 

[Particular U 

QUALITY DISTRIBUTION 

f Affirmative U 

[Negative D 



Meaning and Classes of Implication. The group 
of topics that are now to be discussed, and to which 
the preceding pages are an introduction, is by some 
writers brought together under the title of 'imme- 
diate inferences/ and by others under the title 'in- 
terpretation of propositions/ The objection that is 
usually urged against 'immediate inferences' is that 
an inference always involves the use of a middle 
term, and is therefore mediate; and, consequently, 



264 A TEXT-BOOK OF LOGIC 

that it is a contradiction to speak of 'immediate' in- 
ferences. The objection that may be brought 
against 'interpretation of propositions' is that it 
tends to confuse two different things, namely, the 
import or meaning of propositions, and the question 
of what other statements we are committed to in 
making any statement whatever. We shall speak 
of the 'implications of propositions,' since the ques- 
tions that are to be considered in this chapter relate 
to the various methods of determining the relations 
that exist between our formally expressed proposi- 
tions, and other unexpressed propositions with 
which they are immediately connected. Implication 
etymologically means 'folded-in,' so that the idea 
the topic suggests is that folded within any state- 
ment we make there are other statements that may 
be brought to light by the use of appropriate meth- 
ods. The practical value of this chapter consists in 
the opportunity it affords of finding out that our 
statements ordinarily mean much more than we 
actually express in them. 

We have to consider two main classes of impli- 
cations : 

(1) The Opposition of Propositions. By op- 
position of propositions is meant the relation that 
the truth or falsity of one proposition has to the 
truth or falsity of other propositions dealing with 
the same subject-matter, that is, having the same 
subject and predicate. 

(2) Eductions. By eductions is meant the 
relation that one proposition accepted as true has 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 265 

to other propositions dealing with the same subject- 
matter from other points of view. 

The Opposition of Propositions. The term oppo- 
sition applied to propositions would strictly mean 
that propositions could stand in this relation only 
when the truth of the one involved the falsity of 
the other, and vice versa. This was the original 
meaning and use of the term in logic. But it was 
found convenient to include under the same title a 
consideration of propositions that are not incompat- 
ible with one another. Opposition, as it is now used, 
embraces, therefore, a study of the relations of any 
two propositions referring to the same subject- 
matter whether the truth expressed by one is or is 
not compatible with that expressed by the other. 
Thus, propositions relating to the same subject, but 
differing in quantity, or quality, or both, are said 
to be opposed to each other. 

Since there are only four categorical proposi- 
tions, it is evident that each stands in relation to 
three others. Thus: 

SaP is related to SeP, SiP, SoP. 

SeP is related to SaP, SiP, SoP. 

SiP is related to SaP, SeP, SoP. 

SoP is related to SaP, SeP, SiP. 

If we examine this list of possible oppositions, 
we shall see that each proposition is related to (1) 
a universal proposition, (2) a particular proposi- 
tion, (3) an affirmative proposition, (4) a negative 
proposition. In other words, all propositions are 
related to others (1) of the same and (2) different 



266 A TEXT-BOOK OF LOGIC 

quantity, and (3) of the same and (4) different 
quality. There are, consequently, four kinds of 
opposition in which any proposition may stand. 
Thus, the relation between 

1. Universal propositions of different quality 
is said to be one of contrariety : SaP, SeP. 

2. Universal and particular propositions of the 
same quality is said to be one of subalternation : 
SaP, SiP; SeP, SoP. 

3. Universal and particular propositions of dif- 
ferent quality is said to be one of contradiction: 
SaP, SoP ; SeP, SiP. 

4. Particular propositions is said to be one of 
subcontrariety : SiP, SoP. 

We shall consider each of these kinds of opposi- 
tion in the order in which they have been named; 
and since any statement we make may be either true 
or false, we shall have to examine the propositions 
that stand in opposition on the supposition both of 
their truth and falsity. 

Contrariety. Contrary opposition exists between 
universal propositions of a different quality ; that 
is, between SaP and SeP. Thus, contrary proposi- 
tions differ in quality only. 

If what any universal proposition states is true, 
what its contrary states must be false. For example, 
if it is true that 'All men die,' it is false that 'No 
men die/ If it is true that 'No men are angels,' it 
is false that 'All men are angels.' If, therefore, we 
accept the truth of what either SaP or SeP states, 
the falsity of what its contrary states follows as a 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 267 

matter of course, for the reason that the same pred- 
icates or qualities cannot belong, and not belong, to 
the same subject. On the other hand, if what any 
universal proposition states is false, what its con- 
trary states is left in doubt. If, for example, it is 
false that 'All men are six feet tall,' we are left in 
doubt as to whether 'No men are six feet tall,' be- 
cause some men may be. 

Let us connect these facts with what we have 
already learned. We saw, in the chapter on terms, 
that if two species of a genus differ from one an- 
other more than they do from any of the other co- 
ordinate species, the relation in which they stand is 
one of contrariety. If, for example, within the genus 
G the species S have the characteristic P, then how- 
ever great and numerous the increasing differences 
between one species and another, they cannot be so 
great and numerous that, within the genus, P can 
be denied of any of the species. Based upon the 
degree of their variation from the genus, all the 
species, as we have seen, have a recognised place 
within the genus. But whatever the variations that 
occur, the species are held together by their common 
likeness, and so long as predication is concerned 
with this common likeness, so long can we not en- 
tertain any proposition which denies it of any or of 
all the species of the genus. If SaP is true, the 
proposition that denies that S is P, SeP, must be 
false, and vice versa. 

Let us look at the other case where something 
is falsely predicated of all the species. Now what is 



268 A TEXT-BOOK OF LOGIC 

thus predicated cannot be the genus, for the genus 
can only be predicated truly. If anything is falsely 
predicated, it must be something that is either an- 
other genus, when the statement would be abso- 
lutely false, or something that is or may be a differ- 
entia, when the statement will be partially false. 
If, for example, 'All flesh is grass' were to be inter- 
preted literally, the statement would be false, be- 
cause it predicates a genus that is wholly mislead- 
ing; and if one were to say that 'AH vertebrates 
live in the water,' that would be false, because it 
predicates what is or may be a differentia, some- 
thing that belongs to one of the species though not 
to all of them. In order to detect the falsity in these 
instances, we must know that what is predicated is 
either a wrong genus or a differentia, and this is not 
possible without going beyond what is given in a false 
statement. Hence, if all we know is that P is 
wrongly predicated of S, we cannot say whether P 
belongs in part or not at all to S, and, therefore, can- 
not infer the truth of the contrary of the original 
proposition. The contrary of a false universal, that 
is to say, is involved in doubt. 

Again, the relations of contrary propositions 
may be studied from the side of the denotation 
of their terms. Thus, it cannot be true that 'All' 
and 'None' of the objects denoted by the subject 
term of a proposition have the qualities connoted 
by the predicate term ; the truth of the one excludes 
the truth of the other. That the falsity of one prop- 
osition involves its contrary in doubt may be shown 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 269 

as follows: If some of the objects denoted by the 
predicate term of an affirmative proposition, and 
none of the objects denoted by the same term in a 
negative proposition, belong to the group of objects 
denoted alike by the subject terms of these proposi- 
tions, then it is obvious that in the one case P falls 
partly within, and in the other wholly without, the 
group of objects denoted by the subject terms of 
the two propositions. If, now, we make the state- 
ment falsely that 'All S falls within P without ex- 
hausting it,' we connot affirm truly the contrary of 
this statement, 'No S falls within P,' because there 
is another alternative to the one offered by the con- 
trary, namely, the case where S falls partly within 
and partly without the class of objects denoted by 
P; and which of these two cases is true cannot be 
determined without examining the cases themselves. 
Representing these facts diagrammatically thus : 




SaP SeP SiP 

we must say that if SaP is false, SeP cannot be 
true without disposing of the alternative case SiP. 
But this cannot be done formally, but only by an 
examination of the subject-matter of these propo- 
sitions. 

Subalternation. Subaltern opposition exists be- 
tween a universal and a particular proposition of 
the same quality; that is, between SaP and SiP; 



270 A TEXT-BOOK OF LOGIC 

SeP and SoP. Thus, subaltern propositions differ 
in quantity only. 

If what the universal proposition states is true, 
what its subaltern states is also true. This follows 
from the fact that universal propositions distribute 
their subject terms. Thus, if something is true or 
false, as the universal states, of each of a class of 
objects, it is true or false of any number of them, 
since these must be identical with some of the for- 
mer. The truth, therefore, of the particular is in- 
volved in the truth of the universal proposition. 
Hence, as may be seen by studying the accompany- 
ing diagram, if any part of the S that falls wholly 




SaP 



within P, (SaP), or wholly without P, (SeP), were 
to fall partly without or partly within P, some part 
of S would, in the one case, fall partly within (SiP) , 
and, in the other, partly without (SoP) P, and it is 
of these parts that the statements of the respective 
subaltern propositions is made. 

On the other hand, if what the universal proposi- 
tion states is false, what its subaltern states is left 
in doubt. The truth of the particular is not involved 
in the falsity of the universal, and cannot, there- 
fore, be the ground of the latter's falsity. But, as 
we shall see, it may be. We have studied already 
one ground of falsity of universal statements. We 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 271 

have seen, for example, that when the contrary of 
any proposition is true, that proposition is abso- 
lutely false. But we have also seen that if we start 
with the falsity of a universal statement, nothing 
can be affirmed as to the truth or falsity of its con- 
trary. Now, in contrast to the falsity involved in 
the contrary relation, that involved in the subaltern 
relation is only relative, that is, the falsity may be 
due not to the fact that S-P asserts something con- 
trary to fact, but that it is asserted without regard 
to existing limitations. In other words, since there 
are degrees of error, as well as of truth, SaP and 
SeP may owe their falsity to the fact that only SiP 
and SoP are true respectively. But, here again, if 
we start with the falsity of the universal, we cannot 
say that its subaltern is true or false; truth or 
falsity, in this case, simply remain possible alter- 
natives between which we can decide only by going 
outside what is given in the original proposition. 
And this is equivalent to saying that the subaltern 
is always involved in doubt when all that we know 
is that the universal or subalternans is false. 

What we have seen is that the truth of a univer- 
sal involves the truth of its subaltern ; but that the 
falsity of a universal involves its subaltern in doubt. 

Let us now consider how the universal is affected 
by the truth or falsity of its particular, subaltern, 
proposition. And, first, let us take the case where 
the subaltern is true. If the only thing we know 
about a group of objects is that some of them are 
in a particular place, it is obvious that we cannot 



272 A TEXT-BOOK OF LOGIC 

say that they are all in that place; and the reason 
is not that some are in another place, for that ex- 
ceeds the knowledge contained in the original prop- 
osition, but that some may be. For a similar reason, 
we cannot affirm that 'No trees are in leaf/ if all 
that we know is that 'Some trees are-not in leaf/ 
From the truth of a particular proposition, there- 
fore, we can only conclude that its subalternans — the 
universal of the same quality — is doubtful. Let 
us take, secondly, the case where the subaltern is 
false. Here the falsity of the subaltern involves 
the falsity of the subalternans. Thus, if 'Some apples 
are blue' is false, it is likewise false that 'All apples 
are blue/ and if 'Some apples are-not red' is false, 
it is likewise false that 'No apples are red/ The 
reason for this case is found in the fact that par- 
ticular propositions affirm or deny a predicate of 
certain unspecified objects of a class, and not of the 
class as a whole. If, therefore, we know that a 
statement is false in some case, we know that it 
cannot be true of all cases, since all cases must in- 
clude the case in which it is known to be false. 
Falsus in uno, falsus in omnibus. We are dealing 
here with the exception under which a rule breaks 
down. 

Contradiction. Contradictory opposition exists 
between a universal and a particular proposition 
that differ from each other in quality; that is, be- 
tween SaP and SoP, SeP and SiP. Thus, contradic- 
tory propositions differ both in quantity and quality. 

If what any universal proposition states is true, 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 273 

what its contradictory states must be false. If it 
be true that 'All men are willing to give their lives 
for a cause/ it is false that 'Some men are-not will- 
ing to give their lives for a cause.' If it is true that 
'No men are utterly selfish,' it is false that 'Some 
men are utterly selfish.' If, on the other hand, what 
a universal proposition states is false, what the con- 
tradictory opposite states must be true. For ex- 
ample, if it is false that 'Every man has his price,' 
it is true that 'Some men cannot be bought,' and if 
it is false that 'None of the candidates were suc- 
cessful,' it is true that some were. Further, the 
truth or falsity of particular propositions involves 
the falsity or truth of their contradictories. If 
'Some one is going to get hurt,' is true, it is false 
that 'No one is going to get hurt;' but if the state- 
ment is false, then 'No one is going to get hurt' is 
true. If 'Some people are short sighted' is true, it 
is false that 'No people are short sighted ;' but if it 
is false that 'Some kinds of ignorance promote vir- 
tue,' it is true that 'No kinds of ignorance promote 
virtue.' 

We may express these results in the single state- 
ment that the truth of one of the propositions in 
contradictory opposition involves the falsity of the 
other ; and the falsity of one, the truth of the other. 
Of any pair of contradictory propositions, one must 
be false, and the other true. Contradiction is, there- 
fore, the most complete form of logical opposition. 

Subcontrariety. Subcontrary opposition exists 
between particular propositions of different quality ; 

18 



274 A TEXT-BOOK OF LOGIC 

that is, between SiP and SoP. Thus, subcontrary 
propositions differ in quality only. 

If we make the two statements that 'Some men 
are blue-eyed' and 'Some men are-not blue-eyed/ 
each of these statements is true, and they are in 
subcontrary relation to each other. But the truth 
of either one of them is not sufficient to establish 
the truth of the other. If, for example, we repre- 
sent our two propositions thus: 




SoP 



it will be evident that in each case P, in part or 
whole, is predicated of a different part of S. 
If, consequently, we know that 'Some indeterminate 
number of men are blue-eyed,' (SiP), this is not a 
sufficient ground for saying that the rest are, or are 
not, blue-eyed. The fact that we are dealing with 
particular propositions which have undistributed 
subject terms, that is, terms that do not take into 
account a determinate number of instances of the 
class, but only more or less of them, prevents us 
from saying anything definite of the rest of the class 
with respect to their being or not being blue-eyed. 
Of the propositions, therefore, that exist in subcon- 
trary opposition, we may say that the truth of 
the one leaves the truth of the other in doubt. 

Propositions in the subcontrary relation cannot 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 275 

both be false. In other words, the falsity of one in- 
volves the truth of the other. For example, if it is 
false that 'Some men are four-footed,' it is true that 
'Some men are-not four-footed.' That is, it is only 
on condition that some men are not four-footed that 
we can deny the truth of the statement that 'Some 
men are four-footed.' This view of subcontrary 
opposition is required by the fact that if both par- 
ticular propositions were false, their contradictories 
would both be true; but, as we have seen, SaP and 
SeP cannot both be true, for if one is true the other 
is proved to be false. But if, as we have seen, the 
falsity of the universal — 'All men are four-footed,' 
for example — involves its contrary in doubt, we 
can at least say that its contradictory — 'Some men 
are-not four-footed' — is true. 

The Square of Opposition. The accompanying 
diagram, called the Square of Opposition, is a me- 
chanical devise which has long been traditional in 
logic, and is intended as an aid to the better under- 
standing of the doctrine of opposition. The univer- 
sal propositions are placed at the top, the particular 
propositions at the bottom of the diagram; the 
affirmative propositions are placed on the left, and 
the negative ones on the right. The lines connecting 
any two propositions indicate the kind of opposition 
that exists between them. The top and bottom lines 
which are horizontal and parallel to each other con- 
nect propositions of the same quantity ; the side lines 
which are perpendicular and parallel connect prop- 
ositions of the same quality. The long diagonal lines 



276 



A TEXT-BOOK OF LOGIC 



connect propositions that are different in both quan- 
tity and quality. 




C 
cr 
pa 



Conti 








..cV- 



«? $> 






Subcontraries 



cr 
pa 




Let us now see how it may be used to throw 
light on the doctrine of opposition. It will be ob- 
served at once that every proposition has its con- 
tradictory, and in contradiction, it will be remem- 
bered, we have the most complete form of logical 
opposition. To work the relations of opposition out 
under the control of the contradictory relation seems 
to simplify the whole matter for most students. We 
summarise the doctrine of opposition below, and the 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 277 

student is required to follow the statements out on 
the Square of Opposition. Thus, if 

SaP is true, its contradictory and its contrary- 
are false, and its subaltern is true. 

SaP is false, its contradictory is true, and its 
contrary and its subaltern are doubtful. 

SeP is true, its contradictory and its contrary 
are false, and its subaltern is true. 

SeP is false, its contradictory is true, and its 
contrary and its subaltern are doubtful. 

SiP is true, its contradictory is false, and its 
subcontrary and subalternans are doubtful. 

SiP is false, its contradictory and sub-contrary 
are true, and its subalternans is false. 

SoP is true, its contradictory is false, and its 
subcontrary and subalternans are doubtful. 

SoP is false, its contradictory and sub-contrary 
are true, and its subalternans is false. 

It may be helpful to represent these facts and 
relations diagrammatically. This we may do by 
drawing only so much of the Square of Opposition 
as embodies the relations in which a given proposi- 
tion stands, utilising the arrow head to indicate the 
direction in which given relations are to be read. 
For example, the lines _\J diverge from a common 
point and indicate, according to their direction, the 
propositions we are considering and the relations in 
which they stand. It is obvious that the example 
chosen is the proposition. Since, then, the direc- 
tion of the lines tells us what propositions we are 



278 



A TEXT-BOOK OF LOGIC 



dealing with, and in what relations of opposition 
they stand, we may indicate at the ends of the lines 
whether, in those relations, the proposition is true 
(T), false (F), or doubtful (D). Further, we may 
indicate the original proposition by writing its given 
truth or falsity in a circle. Following these direc- 
tions, we have the accompanying result : 





DD< 



>TT< 




A summary of the doctrine of opposition is given 
in the table on page 279. 

Nature and Methods of Eduction. In the course 
of our study, we have seen that all our judgments 
are related to other judgments referring to the same 
subject-matter, and, consequently, that every judg- 
ment implies more than it asserts. Put more 
directly, every judgment commits us not only to 
what we assert, but also to the acceptance of all 
the other judgments which are implied in what we 
assert. Now when these implied judgments involve 
a change in the point of view from which the sub- 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 279 

ject-matter of the original judgment is viewed, they 
are called eductions. 

We may classify the methods of eduction as ob- 
version, conversion, contraposition, and inversion. 
But only two of these methods, obversion and con- 
version, are fundamental. In the following sections, 
we shall study the fundamental methods first, and 
follow this with a consideration of the derived 
methods, contraposition and inversion. 



Given 


SaP 


SeP 


SiP 


SoP 






F 


T 


F 


oar \ 

I F 




D 


D 


T 


1 T 

q r p J 


F 




F 


T 


( F 


D 




T 


D 


( T 


D 


F 




D 


oil \ 

\ F 


F 


T 




T 


1 T 

Qj-lP / 


F 


D 


D 




oor \ 

I F 


T 


F 


T 





TABLE OF OPPOSITIONS 



Obversion. Other terms by which this method 
is sometimes known are Permutation, Aequipollence, 
Immediate inference by Private Conception. Obver- 
sion is the logical form of the double negative with 
which we have all become acquainted in the study 



280 A TEXT-BOOK OF LOGIC 

of grammar. Like the double negative, it has the 
force of changing an affirmative statement into a 
negative one, and a negative statement into an 
affirmative one. Obversion effects no change in the 
meaning of what is asserted, but only in its em- 
phasis. For example, 'Barkis is willin' ' by obver- 
sion becomes 'Barkis is-not unwillin' ;' To do this 
is-not unnecessary' becomes by obversion To do this 
is necessary.' 

In obversion only the quality of the original 
proposition, called the obvertend, undergoes change ; 
the quantity and the meaning remain the same. But 
if the quality changes, the predicate term of the 
obvertend must also undergo modification if the 
meaning is to remain unaffected. What exactly is 
this modification? It cannot be enough to say that 
the characteristic of the obverse of a proposition is 
that it has for its predicate term the negative of 
the predicate of the proposition from which it is de- 
rived, although, of course, this is, from the formal 
point of view, true. Nor can we say that the con- 
notation of the obvertend is affected, for that is the 
question we are raising. If we are to understand 
the particular significance of obversion, we shall 
have to interpret it as a method that affects the 
meaning of a proposition by a change in what the 
proposition denotes. That is to say, the particular 
range of the objects signified by the obvertend is 
different from that of its obverse. For example, in 
the illustrations used above, it is obvious that 
Barkis' attitude must be one of willingness or un- 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 281 

willingness; and of any action we may say that it 
is necessary or unnecessary. Now, since obversion 
is, in part, a matter of negation, we carry over into 
that process all the characteristics that make nega- 
tion significant. We have seen that negation is very 
largely a matter of the emphasis that we give to 
our knowledge, and of the definiteness or indefinite- 
ness of our acquaintance with what we assert. 
Thus, if we are not sure of the degree of Barkis' 
willingness, we may express the actual state of our 
information or opinion by saying that he is not- 
unwilling. If we wish to suggest, but not to state 
explicitly, the degree of necessity of the things we 
do, we may say that they are not-unnecessary. A 
guarded statement of the latter kind, it will be ob- 
served, becomes more emphatic by obversion, for 
we are thereby led to assert without qualification the 
necessity of our actions. 

There are two steps in the process of obversion ; 
the first consists in changing the quality of the 
original proposition without changing its quantity; 
the second consists in negating the predicate term 
of the original proposition. To consider the first 
step we should observe, with respect to quantity, 
that if the original proposition is universal the de- 
rived proposition is universal, and if the original 
proposition is particular the derived proposition is 
particular; and, with respect to quality, that if the 
original proposition is affirmative the derived prop- 
osition is negative, and that if the original proposi- 
tion is negative the derived proposition is affirm- 



282 



A TEXT-BOOK OF LOGIC 



ative. Combining these two considerations, we find 
that, in obversion, an A proposition always changes 
to an E, an E to an A, an I to an O, and an to an 
I. With regard to negating the predicate term of 
the original proposition, the second step in obver- 
sion, we may observe that if we use a short horizon- 
tal stroke over the symbol of an affirmative predicate 
term to indicate that that term has been negated, 
it will be obvious that obverted propositions are 
characterised generally by having for their predicate 
terms the so-called infinite or non-P term. It fol- 
lows that if the predicate term is already a negative 
or infinite term, the effect of negating it will be to 
remove the sign of negation. The method of indi- 
cating negation by the short horizontal stroke over 
the symbol of an affirmative term is used throughout 
this book, and this fact should be noted; a horizon- 
tal stroke over any term, whether predicate or sub- 
ject term, will have the meaning of negation. Thus, 
S" will mean non-S, M will mean non-M, just as P 
means non-P. With these explanations the method 
of obversion should be sufficiently clear. In the fol- 
lowing table we illustrate the method of obversion in 
each of the four categorical propositions : 



Obvertend 


SaP 


SeP 


SiP 


SoP 


First Step 

Second Step 
Obverse 


SeP 


SaP 


SoP 


SiP 


SeP 


SaP 


SoP 


SiP 



TABLE OF OBVERSIONS 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 283 

Conversion. This is a process by which we affirm 
or deny of the predicate term of an original prop- 
osition, called in this relation the convertend, what 
was asserted by the subject term of the same prop- 
osition. If, for example, we know that 'Pilocarpin 
when taken internally is followed by a slowing of 
the heart beat/ we are able, by conversion, to place 
pilocarpin among the agents which have the effect 
of slowing the heart beat in any investigation we 
may make about the conditions under which the 
heart beat is slowed. In other words, the terms by 
which in one proposition we qualify a subject, may 
themselves become of direct interest to us, and in 
looking about for predicates which shall qualify 
them, we find in the original proposition something 
that is serviceable for this purpose. To state gen- 
erally the fact that conversion denotes, we may say 
that if we make any statement in the S-P form, 
conversion is the answer to the question whether we 
are able, because we have made this statement, to 
make another which will have the form P-S. Hav- 
ing said something about S, can we, therefore, say 
something about P? 

That this is a very reasonable inquiry will ap- 
pear if we recall what was said about the possibility 
of predicating of any term S another P. We saw 
that this possibility rests upon the fact that S is not 
merely S, and that P is not merely P. In any judg- 
ment we are dealing with a complex phenomenon, 
and our statements reflect this fact. We, therefore, 
said that the S that in any proposition is P is an 



284 A TEXT-BOOK OF LOGIC 

SP, and, as we also saw, the P that is predicated 
of S has its roots running down into, and derives 
its character from, the same ground that makes of 
S a significant term. In other words, the P of any 
proposition is also an SP. It is this fact that under- 
lies the process and problem of conversion. If S is 
P at all, then the conditions of its being P are those 
that will enable us to reverse the relation, and to 
declare that P is S. This is the general statement 
of the fact of conversion, but what the limitations 
are under which conversion may legitimately take 
place must be ascertained from the study of con- 
crete cases. In other words, conversion is not a 
wholly formal process, it is not a mere manipulation 
of symbols; but a study of the formal relations of 
the terms of the proposition brings to light some 
of the limits of this type of thinking. 

Formally considered, conversion is the method 
by which the predicate term of one proposition, 
called the convertend, becomes the subject term of 
another, called the converse, and the subject term 
of the former proposition becomes the predicate 
term of the latter. It will be seen, then, that the 
terms of the converse must be the same as the terms 
of the convertend. Stated simply, the terms of the 
converse are derived from the convertend by the 
transposition of its terms : S-P becomes P-S. Again, 
we should observe that in conversion there is no 
change in the quality of the proposition : an affirm- 
ative proposition remains affirmative, and a neg- 
ative proposition remains negative. And, further, 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 285 

the quantity of propositions sometimes is, and some- 
times is not affected by their conversion. This will 
be shown in our examination of the four categor- 
ical propositions, and the reason for it will then be- 
come clear. But before we examine each kind of 
proposition to ascertain whether and in what form 
it is capable of conversion, we wish to call attention 
to the rule which governs all cases of conversion, 
namely: If a term is distributed in the converse 
it must have been distributed in the convertend. 
Practical direction for applying this rule may be 
laid down thus : Quantify the predicate, and trans- 
pose terms. 

The simplest cases of conversion are met with 
in the universal negative and the particular affirm- 
ative propositions: SeP and SiP. The universal 
negative proposition has two distributed terms, and 
the particular affirmative proposition has two un- 
distributed terms. It follows from these facts that 
if we transpose the terms of each proposition, with- 
out changing the quality, no term in the converse 
is distributed that was not distributed in the con- 
vertend. If, for example, the whole of P, in the 
universal negative proposition, lies outside the whole 
of S, then the whole of S falls outside the whole of 
P. In the case of the particular affirmative prop- 
osition, some of S is identical with some of P, and, 
therefore, it follows that the same part of P is 
identical with the same part of S. Under these 
conditions, it is possible not only to say that 'S is 
P,' but also that T is S.' When, as in these two 



286 A TEXT-BOOK OF LOGIC 

cases, we convert a proposition without changing 
its quantity, we are said to convert simply, or, as 
the Latin word has it, simpliciter. 

Conversion by limitation, or per accidens, that 
is, conversion that involves a change in the quantity 
of a proposition, is necessary in the case of the uni- 
versal affirmative proposition, SaP. The reason for 
this is that, being an affirmative statement, the 
predicate term is undistributed, and when this be- 
comes the subject term of a new proposition, it does 
not present a determinate number of objects for the 
predicate to qualify. For example, 'All the books 
are on that shelf cannot imply that 'All the things 
on that shelf are books ;' there may be other things 
on the shelf than books. All, therefore, that we are 
warranted in saying is that 'Some of the things on 
that shelf are books,' a statement that differs in 
quantity from the original proposition. The stu- 
dent may find examples of universal affirmative 
propositions which, on account of the nature of 
their subject-matter, admit of simple conversion; 
but the form of the proposition does not show this. 
'A straight line is the shortest distance between two 
points,' that is to say, definitions, may serve to show 
what is meant. So long, however, as we confine 
attention to the form of the proposition, SaP con- 
verts by limitation to PiS. 

A particular negative proposition cannot be con- 
verted at all. In such a proposition the subject 
term is undistributed, and the predicate term is dis- 
tributed. If, therefore, we transpose the terms, we 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 287 

have a proposition with a distributed subject and 
an undistributed predicate, that is a proposition of 
the form 'All S — some P.' Now the only proposi- 
tion that we have of this form is the universal 
affirmative, and we should be required to take this 
as such a proposition. But this we cannot do, be- 
cause the converse of a proposition must be of the 
same quality as the convertend, and, moreover, no 
negative proposition has an undistributed predicate 
term. But if, in order to overcome this difficulty, 
we were to distribute this term, we infringe the 
rule of conversion which states that if a term is 
distributed in the converse it must have been dis- 
tributed in the convertend. In no way, therefore, 
can we convert a particular negative proposition. 
It may sometimes be true that SoP and PoS are 
both true, but we must go outside the formal rela- 
tions of S and P in the propositions to see this. For 
example, 'Some anarchists are-not Italians,' and 
'Some Italians are-not anarchists' are both true. 
But we do not always get a like satisfactory result 
merely by transposing the terms of particular nega- 
tive statements. For example, 'Some men are-not 
professors' is true, but 'Some professors are-not 
men' is false, so long, that is, as we only mean by 
men membership in the human race. These cases 
depend upon a knowledge of more than the original 
proposition states, and there is no possibility of 
ascertaining the precise nature of that knowledge 
from a study of the formal relations of S and P in 
a particular negative proposition. 



288 



A TEXT-BOOK OF LOGIC 



We add below a table of all possible conversions 



Convertend 


SaP 


SeP 


SiP 


SoP 


Converse 


PiS 


PeS 


PiS 





TABLE OF CONVERSIONS 

Contraposition. Sometimes called Conversion by 
Negation, and Contrapositive Conversion. The con- 
trapositive of a given proposition may be described, 
according to the method by which we arrive at it, 
as the converted obverse. The rule, consequently, 
that we should follow to reach the contrapositive 
of any proposition is: First obvert the original 
proposition, and then convert the proposition thus 
obtained. If we follow this rule, the contrapositive 
will be seen to be a proposition that has for its 
subject term the negative of the predicate of the 
original proposition, called in this case the obver- 

tend. S-P becomes P-S- Now, since ob version is 
involved in the process of reaching a contrapositive, 
and conversion does not change it back again, the 
contrapositive differs in quality from the original 
proposition. And since the quantity of a proposi- 
tion, as we have seen, is sometimes affected by con- 
version, namely, when the proposition is a univer- 
sal affirmative proposition, the quantity of the con- 
trapositive will, in that case, be changed, but in all 
other cases it will be unaffected. 

The contrapositive of any proposition may be 
obverted, and the proposition thus obtained will 
have the characteristics that we have enumerated 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 289 

in the section on obversion. Such a proposition is 
called the obverted contrapositive. In this case 
P-S, the contrapositive of S-P, becomes by obver- 
sion P-S". 

The results of the above statements, expressed 
symbolically, are given in the following table of 
contrapositives : 



Original Proposition 


SaP 


SeP 


SiP 


SoP 


Obverse 


SeP 


SaP 


SoP 


SiP 


Contrapositive 


PeS 


PiS 




PiS 


Obverted Contra 
positive 


PaS 


PoS 




PoS 



TABLE OF CONTRAPOSITION 

Not many examples of contraposition are neces- 
sary if the student has mastered the fundamental 
processes of obversion and conversion. We confine 
ourselves to one: 



Original 
Proposition 


SaP 


All acids are substances that turn 
blue litmus paper red 


Obverse 


SeP 


No acids are substances that do 
not turn blue litmus paper red 


Contrapositive 


PeS 


No substances that do not turn 
blue litmus paper red are acids 


Obverted 
Contrapositive 


PaS 


All substances that do not turn 
blue litmus paper red are non-acid 



19 



EXAMPLE OF CONTRAPOSITION 



290 A TEXT-BOOK OF LOGIC 

Inversion. The inverse of a proposition has for 
its subject the contradictory of the subject of the 

original proposition (invertend). S-P becomes "S-P. 
Like contraposition, inversion is arrived at indi- 
rectly through the use of the two fundamental 
forms of eduction. And since we can obtain by 
obversion the contradictory of a term only when 
that term forms the predicate of a proposition, S 
must be made the predicate of a proposition before 
its contradictory can be ascertained, that is, con- 
version must have taken place at some stage in the 
process of inversion. In other words, S must have 
been made the predicate of a proposition, and then 
that proposition must have been obverted if we are 
to get a non-S term. Inversion can apply only to 
the two universal propositions, SaP and SeP, and in 
each case we get a particular proposition of the gen- 
eral form S-P. We must follow a separate rule in 
each of these cases. To invert a universal affirmative 
proposition, the rule reads: Obvert and convert 
alternately until a proposition of the required form 
is found. The rule for the universal negative prop- 
osition reads : Convert and obvert alternately until 
a proposition of the required form is found. We 
show the necessary steps in each of these cases in 
the following table : 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 291 



Original 
Proposition 


SaP 


Obverse 


SeP 


Converse 


PeS 


Obverse 


PaS 


Converse 


SiP 


Inverse 


SoP 



Original 
Proposition 


SeP 


Converse 


PeS 


Obverse 


PaS 


Inverse 


SiP 



TABLES OF INVERSION 



We may obvert these inverses, and thus obtain 
the obverted inverses. Thus, SoP will give SiP, and 
SiP will give "SoP. It will be "observed that from 
the universal affirmative proposition we get, by in- 
version, a particular negative proposition, and from 
the universal negative proposition a particular 
affirmative proposition, and that by obversion these 
inverses are given the same quality as their re- 
spective original propositions. 

Summary of Eduction. In this section we give 
first an outline schema of the characteristics of the 
propositions arrived at by eduction, that is, we show 
the character and relations of the terms of all the 
eductive propositions. Thus: 



292 



A TEXT-BOOK OF LOGIC 



OriginalProposition S — P 


Obverse ! S-P 


Converse 


P-S 


Contrapositive P— S 


Obverted Contra 
positive 


P-S 


Inverse 


S-P 


Obverted Inverse 


S-P 



SCHEMA OF EDUCTIVE PROPOSITIONS 
In the following table we show, secondly, all the 
eductions of each of the four categorical proposi- 
tions in a form which indicates throughout the 
quantity and quality of the propositions : 



Original Proposition 


SaP 


SeP 


SiP 


SoP 


Obverse 


SeP 


SaP 


SoP 


SiP 


Converse 


PiS 


PeS 


PiS 




Obverted Converse 


PoS 


PaS 


PoS 




Contrapositive 


PeS 


PiS 




PiS 


Obverted Contra 
positive 


PaS 


PoS 




PoS 


Inverse 


SoP 


SiP 






Obverted Inverse 


SiP 


SoP 







TABLE OF EDUCTIONS 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 293 



REFERENCES 

H. A. Aikins, The Principles of Logic, Chs. IX., XL 

J. E. Creighton, An Introductory Logic, 3d Edition, Ch. VII. 

J. G. Hibben, Logic, Deductive and Inductive, Part I., Chs. 
XII., XIIL, XIV. 

W. S. Jevons, Elementary Lessons in Logic, Lessons IX., X. 

J. N. Keynes, Formal Logic, 2d Edition, Part II., Chs. II., 
III., IV., V. 

S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
tion, Ch. III., Parts ii., iii. 

W. Minto, Logic, Inductive and Deductive, Part III., Chs. II., 
III. 

C. Read, Logic, Deductive and Inductive, 3d Edition, Chs. VI., 
VII. 

W. J. Taylor, Elementary Logic, Ch. VIII. 

ADVANCED 

B. Bosanquet, Logic, Ch. VII. 

W. R. B. Gibson, The Problem of Logic, Chs. XIX, XX. 
H. W. B. Joseph, An Introduction to Logic, Chs. IX., X. 
H. Lotze, Logic, Vol. I., Ch. II., §§ 75 to 82. 
F. C. S. Schiller, Formal Logic, Chs. XII., XIII. 
J. Welton, A Manual of Logic, Vol. I., Book III., Chs. II., 
III., §§ 102, 103. 

QUESTIONS. 

1. Classify categorical propositions from the standpoint 
(1) of their quantity and (2) quality. 

2. What are the quantitative and qualitative characteris- 
tics of logical statements. 

3. What symbols are used to distinguish the four categor- 
ical propositions, how are they derived, and what exactly 
do they represent? 

4 Explain what is meant by a structural formula. What 
is the general structural formula of a categorical prop- 
osition? 



294 A TEXT-BOOK OF LOGIC 

6. Write the structural formulae of all the categorical prop- 
ositions, and explain how they are derived. 

6. What do you understand by the distribution of terms? 

7. What determines the distribution of the subject terms 
of propositions? 

8. From what standpoint is the distribution of the pred- 
icate terms of propositions determined? 

9. What is the distribution of each of the terms in each 
of the four categorical propositions? 

10. Explain why the predicate terms of affirmative propo- 
sitions are undistributed. 

XI. Explain why the predicate terms in SeP and SoP are 
distributed. 

12. Classify in any suitable way the distribution of all the 
terms of all the categorical propositions. 

13. What is meant by the implication of propositions? 

14. What other terms have been used to describe the fact 
of implication, and why are these not suitable? 

15. What are the main classes of implication? 

16. What do you understand by the Opposition of Proposi- 
tions? 

17. Name all the relations of opposition of categorical 
propositions. 

18. Between what propositions can the relation of con- 
trariety exist? 

19. How do contrary propositions differ from, and in what 
respects do they argee with, each other? 

20. If one of the propositions existing in a contrary rela- 
tion is true, what can you say of the other? 

21. Explain why a proposition is doubtful if its contrary 
is false. 

22. Between what propositions can the subaltern relation 
exist? 

23. How do subaltern propositions differ from, and in what 
respects do they argee with, each other? 

24. Why does the truth of the subalternans involve the truth 
of the subaltern? 



IMPLICATIONS OF CATEGORICAL PROPOSITIONS 295 

25. Explain why a proposition is doubtful if its subaltern 
is true. 

26. Why is a proposition false if its subaltern is false? 

27. Between what propositions can the contradictory rela- 
tion exist? 

28. How do contradictory propositions differ from, and in 
what respects do they argee with, each other? 

29. Explain why the truth or falsity of a proposition in- 
volves the falsity or truth of its contradictory. 

30. Between what propositions can the subcontrary relation 
exist? 

31. How do subcontrary propositions differ from, and in 
what respects do they argee with, each other? 

32. Why is a proposition doubtful if its subcontrary is true? 

33. Explain why a proposition is true if its subcontrary is 
false. 

34. What is the Square of Opposition? 

35. What are Eductions? 

36. Classify the Eductions. 

37. Explain and illustrate the method of obversion. 

38. Upon what characteristics of propositions does the 
method of conversion rest? 

39. Explain and illustrate the method of conversion. 

40. What is the rule of conversion? 

41. Name and illustrate the classes of conversion. 

42. Why cannot SoP be converted? 

43. Are there any particular negative propositions that 
can be converted? Illustrate. 

44. If your answer to the previous question is in the affirm- 
ative, explain why logic says that SoP cannot be con- 
verted. 

45. What is contraposition? 

46. What steps must be taken to secure the contrapositive 
of a proposition? 

47. Why is the contrapositive of a proposition sometimes 
called the converted obverse? 

48. What is inversion? 



296 A TEXT-BOOK OF LOGIC 

49. What is the method of finding the inverse of SaP? 

50. How do you proceed to find the inverse of a universal 
negative proposition? 

EXERCISES 

Note — State propositions in logical form when answer- 
ing a question, and write the formula for each proposition 
involved in your answers. 

1. Write all the relations of Opposition of: 

(1) We are not all college professors. 

(2) Few books in logic are easy reading. 

(3) The old paths are best. 

(4) Improbable events happen almost every day. 

(5) The longest road comes to an end. 

(6) Unasked advice is seldom acceptable. 

(7) Only ignorant persons hold such opinions. 

(8) Infallibility is a myth. 

2. Give the converse of: 

(1) Mercy but murders, pardoning ( = if it pardons) 
those that kill. 

(2) We cannot all command success. 

3. Give the obverse of: 

(1) Not every advice is a safe one. 

(2) Rivers generally run into the sea. 

4. Give the contrapositive of: 

(1) No one is altogether reliable. 

(2) Every mistake is not a proof of ignorance. 

5. Give the inverse of: 

(1) He that bridleth his tongue is greater than he that 
taketh a city. 

(2) Natives alone can stand the climates of Africa. 



CHAPTER X 

CATEGORICAL ARGUMENTS. 

The Problem of the Chapter. In the previous 
cnapters we have studied mainly the three following 
problems: (1) the nature of simple assertion or 
the judgment, (2) the logical expression of these 
judgments or the proposition, and (3) the problem 
of logical implication. In the next two chapters, 
we shall still be occupied with judgments and their 
propositions; and, although the new problems that 
are to come before us are more complex than those 
we have studied, they will appear simpler, because 
everyone may be presumed to have already some 
acquaintance with them. The fact of common ex- 
perience that underlies the topics of these chapters 
is, that we connect statements of various kinds with 
one another in numerous ways, and that we do 
this with a view to making other assertions that, it 
seems to us, could not be made as surely in any other 
way. Often the actual statements we make are not 
debatable, they are readily accepted by the person to 
whom we are speaking, and may, therefore, be re- 
garded merely as reminding him of certain points 
of common agreement; and if, beyond this simple 
function, they have any use, this must be found in 
what they suggest, and not in what they actually 
state. In other words, we are accustomed to use 
certain significant statements for the purpose of 

(297) 



298 A 1EXT-BO0K OF LOGIC 

making them the bases of certain other significant 
statements which we wish the person to whom we 
are speaking also to accept. Now it is quite obvious 
that about such a general fact as this we may ask 
whether there are any rules of procedure that may 
be followed, if the suggested truth is to be accepted. 
We may ask, that is, whether there are any service- 
able ways of connecting statements when these are 
used as the basis of others the truthfulness of which 
we wish particularly to recommend. This is the 
question we are to consider in this and the following 
chapters, a question that is technically known as the 
problem of the syllogism. To state the problem 
somewhat technically, we are now to enter upon a 
study of the combination of propositions, and of the 
laws of their inter-connection. 

Two Preliminary Questions. Before taking up 
the specific topics to which the present chapter is 
devoted, there are two questions to which some at- 
tention must in the first place be given, — a ques- 
tion about the syllogism, and a question about the 
particular kind of syllogism that we are immediately 
concerned with. About the syllogism we may ask 
whether it is a problem that is set by the judgment, 
by the nature and limitations of human thought, 
and one, therefore, that reveals the structure of the 
thinking or knowing mind ; or, if this is not the case, 
whether it is a problem that grows out of our effort 
to communicate what we know. In the latter case, 
the syllogism is not a problem that is set directly 
by the judgment, but one that arises out of the 



CATEGORICAL ARGUMENTS 299 

nature of the proposition. Now it is not possible, 
nor perhaps is it necessary or desirable, to enter 
into a full discussion of the question thus suggested ; 
but, because of its bearing upon our understanding 
of the nature and function of the syllogism, we may 
point out more specifically that the question really 
asks whether the syllogism is a method by which the 
human mind thinks when it is seeking to gain knowl- 
edge; or whether it is a method by which we lay 
bare, for ourselves and others, the grounds on which 
our knowledge is supposed to rest. That is, we 
are asking whether the syllogism is, as in the one 
case, an instrument for acquiring knowledge; or, 
as in the other, an instrument for the exposition of 
knowledge. In making this statement disjunctive, 
we are not to be understood to mean that the syllo- 
gism may not serve both functions, nor to deny 
that the two functions may be inter-dependent. In- 
deed, what we have seen to be true of the relation 
of the proposition to the judgment, namely, that the 
former, being the expression in words of the latter, 
is controlled by motives that grow out of our desire 
to communicate what we know, may be expected to 
be true also of the syllogism — a series of inter- 
connected propositions — in its relation to the more 
complex process of reasoning. The view that the 
syllogism is a method by which we expound and 
communicate the knowledge that is acquired by 
reasoning seems to have a high degree of probability, 
and it may be allowed, in the main, to determine 
our discussions in the following sections. From this 



300 A TEXT-BOOK OF LOGIC 

point of view, the syllogism will come before us as a 
series of problems connected with the nature and 
connection of propositions, and we must consider 
the present chapter as a continuation of those imme- 
diately preceding it in which we were developing the 
character of propositional statements. 

Turning now to the second inquiry, we may 
raise the question whether we are to study in this 
chapter the connection between any kinds of state- 
ment, and any kinds of connection between state- 
ments. The answer to both parts of the question 
must be, No. There are forms of statement that, 
so long as these forms are retained, do not belong 
to logic at all. We pointed this out above when we 
were studying imperatives, interrogatives, optatives, 
and exclamations. There are also, as we have seen, 
forms of logical statement that are not categorical, 
and which, as we shall see later, present problems 
quite distinct from those that are. Such, for ex- 
ample, are the hypothetical and disjunctive prop- 
ositions. We exclude from the scope of this chap- 
ter both classes of statement, and consider only 
the relationships that hold between categorical 
propositions. There are also kinds of connection 
between categorical statements that are not logical 
in the restricted sense in which we are using the 
word here. Such, for instance, are the connections 
between ideas that the psychologist discusses under 
the head of association. Such, also, are the con- 
nections between ideas based upon the mathematical 
principle of proportion : A is greater than B, B is 



CATEGORICAL ARGUMENTS 301 

greater than C, therefore, A is greater than C. 
Whatever the logical character of these cases may 
be, they do not, on any strict interpretation, belong 
to the present chapter which is confined to a study 
of the connection of categorical propositions which 
is illustrated in the Aristotelian syllogism. 

Nature of the Syllogism. We may describe a 
syllogism as a series of three propositions which are 
related to each other in such a way that the truth 
expressed in one of them, called the conclusion, de- 
pends upon the truth expressed in the other two, 
called the premises, taken together. Let us illus- 
trate this statement in the following simple case: 

All insects are arthropods. 
All bees are insects. 
All bees are arthropods. 

In this syllogism, there are three inter-related prop- 
ositions, each one of which has been written sepa- 
rately. It is obvious to first inspection that the 
truth of the last written statement, 'All bees are 
arthropods/ avowedly rests upon the truth of the 
other two taken together. That is to say, the truth 
of every conclusion is a truth that rests upon a con- 
nection of facts that it requires two propositions, 
at least, completely to express. 

Our understanding of this type of argument will 
be facilitated if we learn to think about the syllo- 
gism from the standpoint of the conclusion it states, 
and not from the standpoint of the premises it ex- 
presses. The reason for doing so is found in the 



302 A TEXT-BOOK OF LOGIC 

nature of the thought processes themselves. In 
these processes, as we saw when studying the judg- 
ment, emphasis is laid primarily upon the answer 
to the cognitive question, What is it? and only sub- 
ordinate importance is attached to the method by 
which the answer is reached. Whether the process 
of thought is relatively simple or complex, sub- 
stantive emphasis is laid upon the solutions that 
are found to the problematic situations that stim- 
ulate the judging activity, and it is the function 
of the conclusions of syllogisms to express such 
solutions. From this point of view, the premises 
must be looked upon as expressing the grounds of 
the fact or truth stated in the conclusion of the 
syllogism. Indeed, it is only as stating the grounds 
of what is expressed in the conclusion that the prem- 
ises are premises at all. In like manner, a con- 
clusion can be a conclusion only if it is regarded as 
the statement of a grounded assertion. The grounds 
of assertion may be relatively simple as in our judg- 
ments of perception; they may be relatively com- 
plex, as in the syllogism; but every judgment is a 
grounded assertion, and when such assertions are 
referred to their grounds, when, that is, the reason 
for holding the assertions is in any way appealed to, 
such assertions are properly called conclusions. 
Premises and conclusions are thus correlative terms, 
and can be understood only from the standpoint of 
their mutual implication. 

Further light is thrown upon the nature of the 
syllogism if we recall that the mental process under- 



CATEGORICAL ARGUMENTS 303 

lying the syllogism is a process of reasoning. The 
mental process underlying the proposition, as we 
have seen, is called a judgment. When, for example, 
we discern the aspects in which objects differ from, 
and are like, each other, directly, that is, by having 
the objects before us and comparing the one with 
the other, this mental process, involving discrim- 
ination, abstraction, and synthesis, is called judg- 
ing, and the mental attitude in which the results of 
such a process is asserted is called a judgment. Now 
the mental process underlying the syllogism is not 
essentially different from that underlying the judg- 
ment. Like the judgment, reasoning rests upon com- 
parison, but unlike it, there is no means of direct 
comparison of one object with another. In this 
case, we compare each of the objects we are trying 
to relate with a third object in order to detect 
whether they have anything in common with it. 
That is, we compare objects, through the observed 
likeness or difference that each has to a third. This 
is called indirect comparison, and the process of 
reasoning in which this is carried out is called me- 
diate reasoning. In contrast to the so-called imme- 
diate reasoning or judgment, mediate reasoning is 
a process underlying the Aristotelian syllogism, and 
we may call the stated results of such a process an 
argument. It is such an argument that gets ex- 
pressed in the syllogism. 

Structural View of the Syllogism. We may, now, 
point out certain characteristics of the syllogism 
that are conditioned by the fact that it is composed 



304 A TEXT-BOOK OF LOGIC 

of a series of interrelated propositions. Proposi- 
tions, for instance, may be said to bear the same 
relation to the syllogism that terms do to the prop- 
osition, that is, they may be regarded as its con- 
stituent elements. But as terms do not form prop- 
ositions by being brought together by the copula, 
so, we may say, the syllogism is not built up by 
the union of propositions. The propositions of a 
syllogism express distinguishable features of a 
complex process of thinking, and it is the purpose 
of the syllogism to make clear the inter-connection 
between the several aspects of our thoughts-about- 
things. In other words, the movement of thought 
in syllogistic reasoning turns upon a common ele- 
ment represented in the syllogism by the middle- 
term, and it is only through this common element 
that there exist grounds for the truth of any medi- 
ated judgment. From this point of view, the middle 
term is as characteristic a feature of the syllogism 
as the copula is of the proposition. 

Certain other features of the syllogism come into 
prominence when we consider it from the stand- 
point of its structure. For instance, every syllo- 
gism has three and only three propositions, — the 
conclusion, and two premises. The conclusion is a 
statement of the relation between two terms which 
are named, from the place they occupy in the syllo- 
gism, the major and minor terms. The subject 
(S) of the conclusion is the minor term of the syl- 
logism, and the predicate (P) of the conclusion is 
the major term of the syllogism. Since now the 



CATEGORICAL ARGUMENTS 305 

premises of a syllogism are propositions, they also 
state a relationship between terms, but not a rela- 
tionship between any terms. Their function is to 
state the relationship that the major and minor 
terms have respectively to a common or middle 
term (M). The proposition that states the rela- 
tionship between the major and middle terms is 
known as the major premise. The proposition that 
states the relationship between the minor and the 
middle terms is known as the minor premise. It 
should be observed that the nature and validity of 
categorical arguments do not depend upon the order 
in which the propositions are named, but upon the 
connection between the propositions of which they 
are comprised. It is usual, however, to write the 
major premise first, the minor premise second, and 
the conclusion last. 

With these facts in mind, it is possible to give a 
definition of the syllogism that emphasises the con- 
nection of the elements that are always present in 
these kinds of arguments. From this point of view, 
the syllogism is a method by which we relate two 
terms (S and P) through the relation that each has 
to a common or middle term (M). 

Rules of the Syllogism. In the previous section, 
we pointed out that the syllogism has a definite 
structure which is determined by the fact that its 
three constituent propositions are related to each 
other through a middle term. The rules of the syl- 
logism may be classified with respect to these facts, 
20 



306 A TEXT-BOOK OF LOGIC 

— with respect to the terms, and with respect to 
the propositions of the syllogism. With respect to 
its terms, the rules are definitely rules of distribu- 
tion. With respect to its propositions, the rules 
refer to the quantity and quality of the propositions. 

RULES OF DISTRIBUTION 

I. The middle term must be distributed in one, 
at least, of the premises. 

II. If a term is distributed in the conclusion, it 
must have been distributed in one of the premises. 

The reason for the first rule is, that the validity 
of the syllogism depends upon the reference of the 
major and minor terms unambiguously to the same 
common term, and this is done with certainty only 
if the middle term is distributed, at least, once. If 
the middle term is undistributed in each premise, 
the major term might be related to one part in the 
major premise, and the minor term to another part 
in the minor premise. Whenever this is the case, 
we have four and not three terms in the two prop- 
ositions, and thus the syllogistic character of the 
argument is destroyed. For example, from the 
statements that 'All rash men are confident,' and 
'All brave men are confident,' we cannot conclude 
that 'All brave men are rash,' for the reason that 
the confidence that each has is or might be a differ- 
ent kind of confidence; there is, in other words, no 
middle term or common factor to serve as a basis 
of comparison. If, however, the middle term is dis- 
tributed in one, at least, of the premises, the part 



CATEGORICAL ARGUMENTS 307 

of the term denoted by the undistributed middle in 
the other premise is included in this distribution, 
and there is thus a common basis of comparison for 
the major and minor terms. Thus, we can affirm 
that 'No Americans are Englishmen' on the ground 
that 'All Englishmen are Europeans,' and 'No Amer- 
icans are.' The fallacy involved in breaking the 
rule for the distribution of the middle term is called 
the fallacy of Undistributed Middle. 

The reason for the second rule is, that we must 
not make a statement, in the conclusion, about a 
determinate number of the objects denoted by a 
term when, in the premises, our statement has been 
about an indeterminate number of these objects. In 
other words, we must not go beyond our accepted 
facts. Stated conversely, to support a conclusion 
which denotes, in either of its terms, a determinate 
number of the objects to which the term applies 
requires that all these objects shall have been denoted 
in one of the premises. When this rule is not ob- 
served by the major term, the fallacy that results is 
an Illicit Process of the Major, and when it is not 
observed by the minor term an Illicit Process of the 
Minor Term. 

RULES OF QUALITY 

I. If the conclusion is affirmative, both prem- 
ises are affirmative; and conversely. 

II. If the conclusion is negative, one premise, 
and only one, is negative; and conversely. 

In discussing these rules, which refer to the 
relation of identity, or of non-identity, of two 
classes, on the ground of their identity or non- 



308 A TEXT-BOOK OF LOGIC 

identity with a third, it is important to observe that 
we can argue a relation of identity only on the basis 
of an identity of relation, and a relation of non- 
identity only on the basis of a non-identity of rela- 
tion. In other words, the relation of S and P to M 
must be either so far identical as to warrant the 
statement of the complete or partial identity of S 
and P; or so far non-identical as to warrant the 
statement of the complete or partial non-identity 
of S and P. If the conclusion is a statement of 
identity, the grounds for such a statement cannot 
be found in a relation of non-identity; nor can we 
find grounds for a statement of non-identity in a 
relation of identity. Hence, if the conclusion is 
affirmative both the premises must be of the same 
quality ; and if the conclusion is negative, one of the 
premises must be of that quality. 

Why can we not ground any statement upon two 
negative propositions? Because, in that case, there 
is no identity of relation between S and M and P and 
M, on which to base such a statement. From the ex- 
clusion of both S and P from M, we cannot argue 
to the identity of S and P, nor can we argue to the 
non-identity of S and P. Two negative premises 
cannot, therefore, support any conclusion, nor can 
any conclusion be inferred from them. 

RULES OF QUANTITY 

I. A particular conclusion cannot be supported 
by two particular premises. 

II. If a conclusion is particular, one, and only 
one, of the premises supporting it can be particular. 



CATEGORICAL ARGUMENTS 309 

With regard to the first rule, let us suppose that 
the particular affirmative, and the particular neg- 
ative, conclusions, SiP and SoP, can be supported by 
two particular propositions. In the former case, the 
premises must be both particular affirmative, and 
then the middle term is undistributed whichever 
place it occupied in the premises. This would give 
the fallacy of the undistributed middle. In the sec- 
ond case, one premise must be particular affirmative, 
and the other particular negative, and then there 
can be only one distributed term, namely, the pred- 
icate of the negative premise. If this is the middle 
term, the major term will be of wider extent in the 
conclusion, which is a negative proposition, than in 
the major premise, — the fallacy of illicit process of 
the major. If, on the other hand, the middle term 
is not the predicate term of the negative premise, 
the argument fails on account of the fallacy of undis- 
tributed middle. 

With regard to the second rule, the particular 
conclusion must be either affirmative or negative. 
If it is affirmative, the premises will both be par- 
ticular affirmative, II., that is, propositions whose 
terms are all undistributed. A syllogism whose 
premises were both particular affirmative would be 
fallacious on account of undistributed middle. If, 
on the other hand, the conclusion were particular 
negative, one of the premises would have to be par- 
ticular negative, 01, 10, that is, propositions only 
one of whose terms is distributed. If this were the 
middle term, then, all the other terms being undis- 
tributed, the conclusion being negative would involve 



310 A TEXT-BOOK OF LOGIC 

the syllogism in an illicit process of the major; and 
if that term were not the middle term, the syllogism 
would involve an undistributed middle. Only one 
premise, therefore, of a particular conclusion can 
be particular. 

Figures of the Syllogism. The propositions that 
together constitute the premises or grounds of a 
syllogism are characterised, as we have seen, by the 
fact that they have a common or middle term. Now 
since each premise has two terms, a subject term 
and a predicate term, and one of these is the middle- 
term of the syllogism, it is obvious that the middle 
term may be either the subject term or the pred- 
icate term of the major premise, and either the 
subject term or the predicate term of the minor 
premise. That is to say, the middle term of a syl- 
logism may occupy four different positions in the 
propositions which, when taken together, are the 
premises of the argument which the syllogism is 
the means of stating. Now the fact that the middle 
term of a syllogism may occupy different positions 
in the premises of different arguments is referred 
to by the term Figure. The Figure of a syllogism, 
in brief, is determined by the position of the middle 
term in its major and minor premises. 

The number of Figures depends upon the num- 
ber of different positions that the middle term may 
occupy alternately in the premises of a syllogism. 
Theoretically, there are four. Thus : 

1. The middle term may be the subject term 
of the major, and the predicate term of the minor 
premise. 



CATEGORICAL ARGUMENTS 



311 



2. The middle term may be the predicate term 
of each premise. 

3. The middle term may be the subject term 
of each premise. 

4. The middle term may be the predicate term 
of the major, and the subject term of the minor 
premise. 

In the order named, the syllogisms whose form 
corresponds to the alternative possibilities just 
named are said to be in the First Figure, the Second 
Figure, the Third Figure, and the Fourth Figure re- 
spectively. Written in outline, syllogisms in these 
Figures will present the following appearance: 



First 


Second 


Third 


Fourth 


Figure 


Figure 


Figure 


Figure 


M— P 


P— M 


M— P 


P— M 


S— M 


S— M 


M— S 


M— S 



S— P 



S— P 



S— P 



S— P 



As an aid to the retention of the positions of 
the middle terms in each of the Four Figures, we 
may add the following suggestion. If we connect 
by a line the middle terms of the premises in the 
Four Figures as just shown in outline, we shall 
get this result: 



II 

M 



M 



III 

M 



M 




312 



A TEXT-BOOK OF LOGIC 



The upper point of these lines is the position occu- 
pied by the middle term of the major premise, and 
the lower point of the lines is the position occupied 
by the middle term of the minor premise in the 
Four Figures respectively. If now to these lines 
we add dotted lines to represent the major and 
minor premises, our diagram will assume this as- 
pect: 




M 



III 

M 



M 




A diagram like this, of course, may mean something 
or nothing according as the student can bring to it 
an interpreting idea. A student informed me that, 
for a number of a class in logic, the two end figures 
were thought of as snakes fighting or hissing at 
each other. The two middle figures were thought 
of as people sitting back to back because they were 
cross with each other. As this information came 
to me two years after the course was taken, it may 
be presumed to have, for one at least, some mne- 
monic value. 

Special Rules of the Four Figures. Each of the 
Four Figures has its own special rules, which are 
applications of the general rules of the syllogism to 
the specific form that categorical arguments as- 
sume in these Figures. We shall state and prove 
the rules for each Figure in order. 



CATEGORICAL ARGUMENTS 313 

FIRST FIGURE 

RULE 1. The minor premise must be affirmative. 

Let us suppose the minor is negative. Then, 

M — P the major must be affirmative, and the 

S — M conclusion negative. Therefore, the major 

term will be undistributed in the major 

S — P premise, and distributed in the conclusion ; 

illicit process of the major. Hence, the 
minor premise cannot be negative, and must be 
affirmative. 
Rule 2. The major premise must be universal. 

If the minor premise is affirmative, the 
middle term is undistributed, and must, 
therefore, be distributed in the major 
premise. And since the middle term is 
subject of this premise, the proposition 
must be universal. 

SECOND FIGURE 

Rule 1. One premise must be negative. 

Since the middle term is the predicate of 
P — M each premise, one of the premises must be 
S — M a negative proposition to avoid the fallacy 

of undistributed middle. 

S— P 

Rule 2. The major premise must be universal. 

The major term being the predicate of a 
negative proposition in the conclusion, is 
distributed. It must, therefore, be dis- 
tributed in the major premise. But since 



314 A TEXT-BOOK OF LOGIC 

there it is the subject of the proposition, 
the major premise must be universal. 

THIRD FIGURE 

Rule 1. The minor premise must be affirmative. 

Let us suppose that the minor is negative. 
M — P Then, the major premise must be affirm- 
M — S ative, and the conclusion negative. There- 

fore, the major term will be undistributed 

S — P in the major premise, being the predicate 

of an affirmative proposition, and distrib- 
uted in the conclusion, being the predicate of a neg- 
ative proposition. This involves illicit major. 
Hence, the minor premise must be affirmative. 

Rule 2. The conclusion must be particular. 

Since the minor premise is affirmative, the 
minor term, being predicate, is undistrib- 
uted, and must, therefore, be undistributed 
in the conclusion also. But the minor term 
is the subject of the, conclusion which, 
therefore, must be particular. 

FOURTH FIGURE 

Rule 1. If either premise is negative, the major 

is universal. 
P — M If either premise is negative, the conclu- 
M — S sion is negative, and the major term of the 

— conclusion must be distributed. It must, 

S, — P therefore, be distributed in the major 

premise. But since there it is the subject, 
the premise must be universal. 



CATEGORICAL ARGUMENTS 315 

Rule 2. If the major premise is affirmative, the 
minor must be universal. 
If the major premise is affirmative, its 
middle term is undistributed. It must, 
therefore, be distributed in the minor 
premise. And since there the middle term 
is the subject, the premise must be uni- 
versal. 
Rule 3. If the minor premise is affirmative, the 
conclusion is particular. 
If the minor premise is affirmative, the 
minor term is undistributed. In the con- 
clusion, therefore, this term must be un- 
distributed. The conclusion, therefore, is 
particular. 
Rule 4. If the minor premise is negative, both 
premises are universal. 
If the minor premise is negative, the minor 
term is distributed. It must, therefore, 
be distributed in the conclusion which will 
then be universal. But a universal con- 
clusion requires two universal premises. 
The Moods of the Syllogism. If now we con- 
sider the structure of the syllogism from the point 
of view of the quantity and quality of the proposi- 
tions which enter into it, we meet with the facts 
which are denoted by the term — the Moods of the 
syllogism. By the Moods of the syllogism is meant 
the character of a syllogism as determined by the 
quantity and quality of its constituent propositions. 
There are, as we have seen, four categorical prop- 



316 A TEXT-BOOK OF LOGIC 

ositions, SaP, SeP, SiP, SoP, and any combination 
of three of these, theoretically, may form the con- 
stituent propositions of a syllogism. For example, 
a syllogism may have in its premises and conclusion 
only universal affirmative propositions. But it may 
have in its major premise a universal affirmative, in 
its minor premise a universal negative, and in its 
conclusion a universal negative proposition. Every 
syllogism must express itself by the use of the four 
categorical propositions three at a time, and, there- 
fore, no syllogism can fail to have a Mood. That is 
to say, each of the constituent propositions of a syl- 
logism has both a quantity and a quality, and when 
we have named the quantity and quality of each 
proposition, in the order of major premise, minor 
premise, and conclusion, we have named the Mood 
of the syllogism. Thus, in the examples just used, 
the mood of the first is said to be AAA, that of the 
second, AEE. 

The Valid Moods of the Syllogism. The Mood of 
a syllogism, we have said, is determined by the 
quantity and quality of its constituent propositions. 
The question that now comes before us is, How many 
of the possible combinations of three out of the four 
categorical propositions, taken as major and minor 
premise and conclusion, will give us valid moods, 
that is, syllogisms whose conclusions logically de- 
pend upon the premises on which they are said to 
rest? In answering this question, it will simplify 
our task if, leaving the conclusions out of consider- 
ation, we ascertain the combinations of propositions 



CATEGORICAL ARGUMENTS 317 

which are possible as premises. Since, as we have 
seen, there are four categorical propositions, each 
of these may serve successively as the major prem- 
ise of a syllogism, and each may serve successively 
as the minor premise of the same syllogism. Thus, 
writing the major premise first and the minor sec- 
ond, we shall get the following sixteen combina- 
tions : 



AA 


EA 


IA 


OA 


AE 


EE 


IE 


OE 


AI 


EI 


II 


01 


AO 


EO 


10 


00 



If, now, we examine this list of possible prem- 
ises, it is apparent that some must be rejected by 
the rules of the syllogism that we have stated in 
another section. Certain combinations are disqual- 
ified because they violate the rule against negative 
premises, for example, EE, EO, OE, and 00; cer- 
tain others must be eliminated because they offend 
against the rule about particular premises, for ex- 
ample, II, 10, and 01. There remain, after the dis- 
qualified members have been eliminated, the follow- 
ing combinations : 

AA EA IA OA 

AE IE 

AI EI 

AO 

These we must consider as the only premises that 
can be appealed to in support of any conclusion 
which we may be concerned to maintain. 



318 A TEXT-BOOK OF LOGIC 

Relation of Moods to Figure. There is, however, 
a further question that requires an answer, namely, 
whether we can throw the defence of a conclusion 
upon any of the above-mentioned premises in any 
of the Figures without affecting the validity of the 
argument. Or, to state the same question con- 
versely, Is each of the above pairs of premises ca- 
pable of rendering a valid conclusion in each of the 
Four Figures? We are asking, what effect, if any, 
the statement of a syllogism in either of the Four 
Figures has upon the validity of the argument. 

There are two methods that may be adopted in 
seeking an answer to this question. And first we 
shall examine each of the above combinations of 
premises in the light of the special rules of each 
Figure, accepting those that conform, and rejecting 
those that do not conform to the requirements of the 
particular Figure. 

In the First Figure, the major premise must be 
universal, and the minor affirmative. The only com- 
binations of premises that stand these tests are, AA, 
Al, EA, and EL If we draw the proper conclusion 
in each case, we may write the four valid moods 
for this figure as follows : 

AAA All EAE EIO 

It will be observed that in this figure we are able 
to support by premises a conclusion stated in any 
one of the four propositions A, E, I, and O. 

In the Second Figure, the major premise must 
be universal, and one premise negative. The only 



CATEGORICAL ARGUMENTS 319 

combinations of premises that satisfy these require- 
ments are AE, AO, EA, and EI. With their respect- 
ive conclusions, these premises give the following 
Moods : 

AEE AOO EAE EIO 

The conclusions in the Second Figure, it will be ob- 
served, are negative propositions, either E or 0. 

In the Third Figure, the minor premise must be 
affirmative, and the conclusion particular. The fol- 
lowing are the combinations of premises in which 
the minor is affirmative : AA, AI, EA, EI, IA, and 
OA. From each of these we may draw, as required, 
particular conclusions, and the valid Moods will be 
as follows: 

AAI All EAO EIO IAI OAO 

In the Fourth Figure, if either premise is neg- 
ative, the major is universal; if the major premise 
is affirmative, the minor is universal; if the minor 
premise is affirmative, the concluson is particular, 
and if the minor is negative, both premises are uni- 
versal. The only combinations of propositions 
which satisfy these conditions are: AA, AE, EA, 
EI, IA. To draw conclusions from these premises, 
we must remember that when, in this figure, the 
minor premise is affirmative, the conclusion must be 
particular. The valid moods are : 

AAI AEE EAO EIO IAI 



320 A TEXT-BOOK OF LOGIC 

In this figure, we may support conclusions stated in 
each of the four propositions, excepting the univer- 
sal affirmative. 

The second method of determining the valid 
Moods is to examine each of the combinations of 
premises in each Figure, and observe whether it 
satisfies the requirements of a valid argument. 
Since we have eliminated those combinations of 
premises which do not meet the rules of quantity 
and quality as stated above, the validity of the argu- 
ment will depend upon its satisfying the rules of 
distribution. We shall give examples below for all 
the Figures, and the student is urged to work out 
the entire list. This will be a review exercise, and 
it will help him to fix definitely the essentials con- 
nected with the Figure and Mood of syllogisms, and 
the distrbution of terms. 

To begin, we may write the structural formulae 
for the Figures in which we are to examine the given 
combination of premises. Thus: 

I II III IV 

M— P P— M M— P P— M 



S— M S— M M— S M— S 



S— P S— P S— P S— P 



In the vacant spaces of each premise may be written 
the combination of premises we are wishing to ex- 
amine, and in the vacant space of the conclusion, 
the conclusion that these premises support. 

When this has been done, our first question will 
be : Is the middle term distributed in one, at least, 



CATEGORICAL ARGUMENTS 321 

of the premises? The second question will be: Is 
each distributed term of the conclusion, when there 
is one, distributed also in one of the premises? 

We give the following examples chiefly as a 
guide to the student in working out the entire list. 
AE in all the Figures. 

I II III IV 

MaP PaM MaP PaM 

SeM SeM MeS MeS 



SeP SeP SeP SeP 

In the First Figure, this argument is invalid be- 
cause the major term is distrbuted in the conclusion 
and is not distributed in the major premise: Illicit 
process of the major. 

In the Second Figure the argument is valid. 

In the Third Figure the argument is invalid be- 
cause the major term is distributed in the conclusion 
and is not distributed in the major premise : Illicit 
process of the major. 

In the Fourth Figure, the argument is valid. 
AI in all the Figures. 



I 


II 


III 


IV 


MaP 


PaM 


MaP 


PaM 


SIM 


SiM 


MiS 


MiS 



SiP SiP SiP SiP 

In the First Figure, the argument is valid. 

In the Second Figure, the argument is invalid 
because the middle term is not distributed in either 
premise : Undistributed middle. 
21 



322 A TEXT-BOOK OF LOGIC 

In the Third Figure, the argument is valid. 

In the Fourth Figure, the argument is invalid 
because the middle term is not distributed in either 
premise: Undistributed middle. 

REFERENCES 
H. A. Aikins, The Principles of Logic, Chs. XII., XIIL, XIV., 

XV., XVI. 
J. E. Creighton, An Introductory Logic, 3d Edition, Chs. 

VIII., IX. 
J. G. Hibben, Logic, Deductive and Inductive, Part I., Chs. 

XV., XVI. 
W. S. Jevons, Elementary Lessons in Logic, Lessons XV., 

XVI. 
J. N. Keyes, Formal Logic, 2d Edition, Part III., Chs. I., III., 

V. 
S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
tion, Ch. VI. 
W. Minto, Logic, Inductive and Deductive, Part IV., Chs. I., 

II., III., IV. 
C. Read, Logic, Deductive and Inductive, Chs. IX., X. 
W. J. Taylor, Elementary Logic, Chs. IX., XL 

ADVANCED 

F. H. Bradley, The Principles of Logic, Book I., Chs. III., 

VII., VIII. 
W. R. B. Gibson, The Problem of Logic, Chs. XXL, XXII., 

XXIII., XXIV., XXV. 
H. W. B. Joseph, An Introduction to Logic, Chs. XII., XIIL, 

XIV. 
H. Lotze, Logic, Vol. I., Book I., Ch. III. 
J. S. Mill, A System of Logic, Book II., Chs. II., III. 
F. C. S. Schiller, Formal Logic, Chs. XIV., XV., XVI. 
C. Sigwart, Logic, Vol. I., Part II., Ch. III., §§ 54, 55, 59. 
J. Venn, Empirical Logic, Ch. XV. 
J. Welton, A Manual of Logic, Vol. L, Book IV., Chs. I., II., 

III. 



CATEGORICAL ARGUMENTS 323 

QUESTIONS 

1. In what respects are the problems of this and the im- 
mediately following chapters related to those of the pre- 
ceding chapters? 

2. What general view of the syllogism is assumed in the 
discussions of this chapter? 

3. What particular forms of statement are and what are 
not studied in this chapter? 

4. Discuss the advantages and disadvantages of viewing 
the syllogism from the standpoint (1) of its premises 
and (2) of its conclusion? 

5. What mental process underlies the syllogism, and how 
does it differ from that which underlies the judgment? 

6. What do you understand by the major, minor and mid- 
dle terms of the syllogism? 

7. Define the syllogism from the standpoint of its con- 
tained terms. 

8. Define and illustrate the following: Premise, Conclu- 
sion, Major premise, Minor premise, Undistributed mid- 
dle, Illicit process. 

9. With respect to what aspects of its contained proposi- 
tions are the rules of the syllogism determined? 

10. Explain why the middle term of a syllogism must be 
distributed in at least one of the premises. 

11. Why is there no separate rule relating to a term in the 
conclusion that is undistributed? 

12. Why must the premises of an affirmative conclusion be 
affirmative? 

13. Explain why a negative conclusion can be supported 
only if but one of its premises is negative. 

14. Why cannot a particular conclusion be supported by two 
particular premises? 

15. What is meant by the Figure of a syllogism? 

16. Describe the formal characteristics of each of the Fig- 
ures. 

17. What do you understand by the Special Rules of the 
Four Figures? 



324 A TEXT-BOOK OF LOGIC 

18. What is meant by the Moods of the syllogism? 

19. How do you determine all the theoretically valid Moods 
of the syllogisms? 

20. What is the relation of the Moods to the Figures of the 
syllogism? 

21. What two methods may be adopted to determine whether 
a particular argument is valid in a given Figure? 

EXERCISES 

Note — Write the formula for each proposition and syl- 
logism in your answers to the following questions. 

1. Point out (1) the conclusion, (2) the middle term, (3) 
the major term, (4) the minor term, (5) the major pre- 
mise, (6) the minor premise in the following argu- 
ments : 

(1) The receiver of stolen property should be punished; 
you have received stolen property, and, therefore, 
should be punished. 

(2) Theft is crime; theft was encouraged by the laws 
of Sparta, therefore, the laws of Sparta encouraged 
crime. 

(3) Only those messages which have been prepaid will 
be delivered; this message has been prepaid, and, 
therefore, will be delivered. 

2. Name all the rules of the syllogism which are broken 
by each of the following Moods: 

AIA, EEI, IEA, IOI, IIA, AEI. 

3. Prove from the rules alone, irrespective of Figure, that 
IE can yield no valid conclusion. 

4. In what Figures do the following premises yield a valid 
conclusion : 

AA, AI, EA, OA. 

5. Why cannot a particular negative proposition stand (1) 
as a premise in the First, (2) as a major in the Second, 
(3) as a minor in theThird, or (4) as a premise in the 
Fourth Figure? 



CATEGORICAL ARGUMENTS 325 

6. Arrange the following arguments in the order of major 
and minor premise, and conclusion, and determine their 
Figure, Mood, and validity: 

(1) All colours are physical phenomena, but no sounds 
are colours, and therefore no sound is a physical 
phenomenon. 

(2) Whatever is given on the evidence of sense may be 
taken as a fact; the existence of God, therefore, is 
not a fact, for it is not evident to sense. 

(3) Every candid man acknowledges merit in a rival; 
every learned man does not do so; therefore, every 
learned man is not candid. 

7. What can be determined respecting a syllogism under 
each of. the following conditions: 

(1) That only one term is distributed, and that only 
once. 

(2) That only one term is distributed, and that twice. 

(3) That two terms only are distributed, each only once. 

(4) That two terms are distributed, each twice. 



CHAPTER XI 
OTHER FORMS OF CATEGORICAL ARGUMENT 

Their Relation to the Syllogism. The syllogism 
may be considered from either of two points of view, 
from the point of view of its premises, or from the 
point of view of its conclusion. If we attend par- 
ticularly to the premises, we shall think of the syllo- 
gism as a method by which from given data we 
arrive at a conclusion; if we attend particularly to 
the conclusion, we shall think of the syllogism as a 
method by which we state the grounds on which 
a position already arrived at is held to rest. These 
two ways of regarding the syllogism are not con- 
tradictory, nor is our view of the nature of the syl- 
logism affected by the possibility of this two-fold 
approach to its problems. There results only a 
slightly different emphasis in one's exposition; in 
the one case, the conclusion, in the other, the prem- 
ises, come to be the focus of our logical interest. 

The reason why we may alter, in the way just 
indicated, our exposition of the syllogism is that the 
syllogism does not express a series of consecutive 
steps by which the judgment actually proceeds for- 
ward from data to conclusion, or backward from 
conclusion to grounds; but it represents, in a con- 
ventional form and order, the simplest inter-connec- 
tions of a complex process of reasoning. It is some- 
times brought forward as an objection to syllogistic 

(326) 



OTHER FORMS OF CATEGORICAL ARGUMENT 327 

reasoning that it is not an instrument of the dis- 
covery of truth ; but the objection rests upon a mis- 
understanding. The truth about any subject-matter 
is discovered by thinking, and the syllogism is not, 
and does not affect to be, a substitute for thinking. 
We may even say that unless truth already exists, 
unless some kind and degree of thinking has taken 
place, the syllogism has no function to perform. 
The syllogism presupposes the existence of truth, 
and is not the condition of its existence. It repre- 
sents the results of our reflection upon the truth 
that is already in our possession, — a reflection that 
is directed towards finding out the reasons why 
truth assumes a demonstrative character. Now this 
is not a small nor an easy thing. It is, however, an 
eminently practical thing. For when thought takes 
itself to task, and, by reflection upon its own proc- 
esses, demands that the conditions of truth be 
erected into principles of demonstration, we may be 
led to see how far from being demonstrative are 
many of the beliefs that we hold most confidently. 

These remarks have a practical bearing upon 
the subjects of this chapter, and may prepare us to 
understand why our thoughts-about-things can be 
thrown into a variety of forms which conform in 
principle only to the Aristotelian syllogism. The 
discussion of these arguments should lead us to see 
that even in logic we are not bound in the state- 
ment of our thought to the formal primness of the 
three-term syllogism. 



328 A TEXT-BOOK OF LOGIC 

Enthymeme. This is the name of a categorical 
argument which omits, in statement, one of the con- 
stituent factors of the syllogism. Now since there 
are three propositions, two premises and a con- 
clusion, in a categorical syllogism, the omission of 
either one of these from the syllogism results in an 
enthymeme. But it must not be supposed that the 
omission of one member of a syllogism destroys the 
syllogistic character of the reasoning, for, as the 
term itself implies, the omitted member still func- 
tions in the mind of the person who states his 
thought in this particular form. The enthymeme, 
consequently, is a particular way of stating a cat- 
egorical argument, it is not a new form of categor- 
ical syllogism. 

According as the omitted member of the syllo- 
gism is the major premise, the minor premise, or 
the conclusion, the resulting enthymeme is said to 
be of the First Order, the Second Order, and the 
Third Order respectively. An enthymeme of the 
First Order, consequently, is a syllogism which is 
abbreviated by the omission of the major premise. 
For example, Those who have no occupation have 
nothing in which to interest themselves, and are, 
therefore, unhappy.' An enthymeme of the Second 
Order is a syllogism which is abbreviated by the 
omission of the minor premise. For example, 'Those 
who have no occupation are unhappy, because they 
have nothing in which to interest themselves.' An 
enthymeme of the Third Order is a syllogism which 
is abbreviated by the omission of the conclusion. 



OTHER FORMS OF CATEGORICAL ARGUMENT 329 

For example, Those who have nothing in which to 
interest themselves are unhappy, and those who 
have no occupation have nothing in which to interest 
themselves/ 

In the enthymeme, as in the fully expressed 
syllogism, the order in which the propositions are 
stated is wholly a matter of convenience, and does 
not affect the nature or validity of the argument. In 
case of the enthymeme, however, it must be made 
obvious by the use of such words as 'and,' 'because,' 
and 'therefore,' which members of the syllogism we 
are undertaking to express. 

It may be questioned whether the enthymeme 
has both Mood and Figure. Perhaps the best 
answer to this inquiry would be that a syllogism in 
any Figure and Mood may be stated as an enthy- 
meme by the omission of one of its constituent prop- 
ositions. But since Mood and Figure are character- 
istics of arguments only when fully expressed in the 
three-term syllogism, the most that we can say is 
that an enthymeme implies a Figure and Mood, and 
not that it has either. 

Polysyllogism. In the enthymeme, we have an 
example of the elliptical character of thought. Think- 
ing, indeed, is ordinarily carried on by means of the 
smallest number of factors necessary to its success 
definitely present to consciousness. When the 
thought is a simple one, and the inter-connection of 
its parts consists of a relation of three terms, any 
one of the relations may fall into the background 
without invalidating or making doubtful its truth. 



330 A TEXT-BOOK OF LOGIC 

This is, as we have seen, the case of the enthymeme. 
When, however, thinking becomes complex, and the 
inter-connection of its parts involves relations of 
many terms, it is much more necessary to simplify 
our methods, if thinking is not to break down under 
the weight of the terms into which the subject- 
matter of thought is analysed. In this case, what 
we do is to build up a series of enthymemes or 
abbreviated syllogisms, and such a series is called 
a polysyllogism. A polysyllogism is, therefore, a 
series of inter-connected enthymemes representing a 
continuous chain of reasoning. 

It is customary to denote the syllogisms into 
which a polysyllogism may be analysed by the terms 
prosyllogism and episyllogism. The application of 
these terms depends entirely upon whether we are 
thinking of the constituent syllogisms in the for- 
ward direction, that is, of the first syllogism as 
being connected with the second, and the second 
with the third, etc. ; or whether we are thinking of 
them in the reverse order, that is, of the second 
syllogism as being connected with the first, the 
third with the second, etc. When we think of the 
constituent syllogisms in the former way, each syl- 
logism is called a prosyllogism; and when we think 
of them in the latter way, each syllogism is called 
an episyllogism. The terms prosyllogism and epi- 
syllogism, consequently, are used relatively, and any 
syllogism in a train of reasoning may be both a pro- 
and an episyllogism. It is obvious that the first 



OTHER FORMS OF CATEGORICAL ARGUMENT 331 

syllogism in such a series can be only a prosyllogism, 
and the last only an episyllogism. 

Types of Polys yllogism Trains of reasoning 
of the type just described fall into two main classes, 
progressive and regressive. We shall describe each 
of these briefly, and merely for the purpose of show- 
ing their logical structure. 

A progressive, synthetic, or episyllogistic train 
of reasoning proceeds from the premises of a pro- 
syllogism to the conclusion of an episyllogism. A 
polysyllogism of this character develops progress- 
ively the consequences of the premises which form 
its starting point. Stated otherwise, the progressive 
polysyllogism advances from the conditions to what 
is conditioned, from causes to effects. Probably 
the most familiar illustrations of this class of poly- 
syllogism for the student are to be found in the 
direct proofs of geometrical propositions. A re- 
gressive, analytic, or prosyllogistic train of reason- 
ing proceeds from the conclusion of an episyllogism 
to the premises of a prosyllogism. In such cases 
we go back from a conclusion to show the grounds 
upon which it rests. Stated otherwise, we are said 
to reason from the conditioned to its necessary con- 
ditions, from effects to causes. 

Illustrations of these two classes of polysyllo- 
gisms will be found in the following sections in which 
we consider the various forms that such trains of 
reasoning may assume. In this and the preceding 
section we have been considering the general charac- 
teristics of a group of syllogisms; in the sections 



332 A TEXT-BOOK OF LOGIC 

that follow we are to study the cases that fall under 
one or other of the two main classes of the group. 

Sorites. This is a polysyllogism whose constitu- 
ent syllogisms are all in the First Figure, and from 
which all the conclusions, except the last, are omit- 
ted. Or, since a syllogism which omits one of its 
propositions is an enthymeme, we may regard a 
sorites as a series of enthymemes from each of 
which, except the first, one premise is omitted, and 
from each of which, except the last, the conclusion 
is omitted. 

There are two forms of sorites, progressive and 
regressive, which are usually distinguished as the 
Aristotelian and the Goclenian respectively. An ex- 
amination of each of these will serve to set the 
nature of this class of arguments more clearly in 
the light. 

An Aristotelian sorites is a progressive series of 
enthymemes in which the omitted conclusion of each 
prosyllogism forms the minor premise of the suc- 
ceeding episyllogism. A familiar example may be 
taken from Rom. VIII., 29, 30 : 'For whom he fore- 
knew, he also foreordained to be conformed to the 
image of his Son, . . . and whom he foreordained, 
them he also called; and whom he called, them he 
also justified: and whom he justified, them he also 
glorified.' A Goclenian sorites — so called from Pro- 
fessor Goclenius of Marburg (1547-1628) its dis- 
coverer — is a regressive series of enthymemes in 
which the omitted conclusion of each prosyllogism 
forms the major premise of the succeeding episyl- 



OTHER FORMS OF CATEGORICAL ARGUMENT 333 

logism. For example: 'One must take pains if he 
is to be a successful man; industry is necessary to 
taking pains ; health is necessary to industry ; a reg- 
ulated diet and sufficient recreation and rest are 
necessary to health ; and, therefore, a regulated diet 
and sufficient recreation and rest are necessary if 
one is to become a successful man.' 

The symbolic expression and analysis of each 
of these forms of sorites may be given thus : 

ARISTOTELIAN SORITES 



S is 


A 




A is 


B 




B is 


C 




C is 


P 




S is 


P 




Analysis : 






S 


is 


A 


A 


is 


B 


f(S 


is 


B) 


1 B 


is 


C 


l(S 


is 


O 


c 


is 


p 


s 


is 


p 



GOCLENIAN SORITES 


z 


is P 


Y 


is Z 


X 


is Y 


S : 


is X 


S 


is P 


Z is 


P 1 


Y is 


■ Z L 


( (Y is 


P)J 


i Z is 


Y 


( (X is 


P>1 


S is 


x \ 


S is 


P 1 



Each of these forms is subject to special rules 
which we shall proceed to state and prove. 

THE SPECIAL RULES OF THE ARISTOTELIAN SORITES 

Rule 1. Only one premise, and that the last, 
can be negative. 

Let us suppose that two of the premises are neg- 
ative. Then the conclusion of the syllogism in 



334 A TEXT-BOOK OF LOGIC 

which the first negative premise occurs will be neg- 
ative. But since this negative conclusion is neces- 
sarily a premise of the next succeeding syllogism, 
its concluson will be negative, and so on, until a 
negative conclusion enters as a premise into a syl- 
logism which has the second negative premise. But 
as we have seen, from two negative premises no 
conclusion can be inferred. Only one premise, there- 
fore, can be negative. 

This negative premise must be the last. Let us 
suppose that some other premise is negative. In 
that case, the conclusion of the syllogism into which 
it entered would be negative. This conclusion, serv- 
ing as the minor premise of the following episyllo- 
gism, would give a conclusion that is negative, that 
is, one in which the major term is distributed. But 
since the major term in the affirmative major prem- 
ise is undistributed, the argument would fail on ac- 
count of an illicit process of the major. No premise, 
therefore, except the last can be negative. 

Rule 2. Only one premise, and that the first, 
can be particular. 

Since every premise, except the last, must be 
affirmative, it is evident that the conclusions of the 
constituent syllogisms, except the last, must be 
affirmative. If now the first premise is particular, 
the conclusion of the first prosyllogism will be par- 
ticular. And if any other premise, except the first, 
were particular, there would occur somewhere in the 
series two particular affirmative premises, and this, 



OTHER FORMS OF CATEGORICAL ARGUMENT 335 

in the First Figure, involves the fallacy of undis- 
tributed middle. 

THE SPECIAL RULES OF THE GOCLENIAN SORITES 

Rule 1. Only one premise, and that the first, 
can be negative. 

If more than one premise were negative, one of 
the constituent syllogisms would be involved in the 
fallacy of negative premises. And since, if any 
premise is negative, the conclusion must be negative, 
that premise must be the one which contains the 
predicate term of the conclusion, that is, the first 
premise in this particular case. 

Rule 2. Only one premise, and that the last, 
can be particular. 

If any premise is particular, the conclusion of 
the syllogism in which it occurs would be particular ; 
and if this conclusion became a premise of another 
syllogism whose premise was already particular, 
there would be involved, in the First Figure, the fal- 
lacy of undistributed middle. Only the last premise, 
therefore, can be particular. 

Epicheirema. This is a regressive chain of 

reasoning in which one, or both, of the premises is 
expanded by the addition of a reason. In other 
words, it is an argument in which one of the prem- 
ises is an enthymeme, but in which both may be. 
If only one of the premises is supported by a reason, 
the epicheirema is called single, and when both are 
so supported, double. A single epicheirema, there- 



336 A TEXT-BOOK OF LOGIC 

fore, is a regressive chain of reasoning in which 
one of the premises is supported by a reason. For 
example : 

All rational beings are to be treated with respect, inas- 
much as they are made in the image of God. 
Slaves are rational beings. 
Therefore, slaves are to be treated with respect. 

— Father Clarke. 

A double epicheirema is a regressive chain of 
reasoning in which both premises are supported by 
a reason. For example : 

All Malays are cruel, because all savages are. 

All the aboriginal inhabitants of Singapore are Malays, 

because all the natives of that part of Asia are. 
Therefore, all natives of Singapore are cruel. 

— Welton. 

The formulae for these two kinds of epicheirema 
may be written as follows : 

SINGLE DOUBLE 

Every M is P, because it is X Every M is P, because it is X 
Every S is M Every S is M, because it is Y 

Every S is P Every S is P 

REFERENCES 

J. E. Creighton, An Introductory Logic, 3d Edition, Ch. X. 

J. G. Hibben, Logic, Deductive and Inductive, Part I., Ch. 
XVIII. 

W. S. Jevons, Elementary Lessons in Logic, Lesson XVIII. 

J. N. Keynes, Formal Logic, 2d Edition, Part III., Ch. VI. 

S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
tion, Ch. VI., §§ 11-13. 



OTHER FORMS OF CATEGORICAL ARGUMENT 337 

W. Minto, Logic, Inductive and Deductive, Book I., Part IV., 

Ch. V. 
C. Read, Logic, Deductive and Inductive, 3d Edition, Ch. XI. 
W. J. Taylor, Elementary Logic, Ch. XIII. 

ADVANCED 

W. R. B. Gibson, The Problem of Logic, Ch. XXIX. 
H. W. B. Joseph, An Introduction to Logic, Ch. XVI. 
J. Welton, A Manual of Logic, Vol. I., Book IV., Ch. VI. 

QUESTIONS 

1. What characteristic of human thinking underlies the 
forms of argument studied in this chapter? 

2. What is an Enthymeme? 

3. Name and illustrate the distinct types of Enthymeme. 

4. How do we know whether any expressed proposition of 
an Enthymeme is major or minor premise or conclusion? 

5. Do Enthymemes have Figure and Mood? Explain. 

6. What is a Polysyllogism? 

7. Under what conditions does human thinking assume a 
polysyllogistic form? 

8. Explain and illustrate the meaning of the terms Pro- 
syllogism and Episyllogism. 

9. Describe and illustrate the general characteristics of a 
Progressive Polysyllogism. By what other names is it 
known? 

10. Describe and illustrate the general characteristics of a 
Regressive Polysyllogism. By what other names is it 
known? 

11. What is a Sorites? 

12. Describe and illustrate the character of an Aristotelian 
Sorites. Write also its structural formula. 

13. Describe and illustrate the character of a Goclenian So- 
rites. Write its structural formula, 

22 



338 A TEXT-BOOK OF LOGIC 

14. What is an Epicheirema? 

15. Explain and illustrate each type of Epicheirema, and 
write the formula. 

EXERCISES 

Note — Write the formula for each of the propositions 
and syllogisms contained in your answers to the following 
questions. 

1. What is the logical character of the following argu- 
ments : 

(1) He must have committed the murder, for he was the 
only person present with the deceased at the time. 

(2) Nations are justified in revolting when badly gov- 
erned, for every people has a right to good govern- 
ment. 

(3) Death cannot be an evil, for it is universal. 

(4) The planet Mars resembles the earth in possessing 
atmosphere, water, and moderate temperatures, 
and these conditions on the earth are necessary to 
its being inhabited. 

(5) He must be mad to do such a thing. 

2. What is the logical character of the following argu- 
ments : 

(1) Misfortunes sometimes are circumstances tending to 
improve character, circumstances tending to im- 
prove character are promoters of happiness, what 
tends to promote happiness is for the general well- 
being, therefore, misfortunes sometimes promote 
general well-being. 

(2) A wise man is one who seeks to gain knowledge, the 
man who seeks to gain knowledge must be indus- 
trious, the industrious man has to make sacrifices, 
to make sacrifices is always a hardship, and, there- 
fore, a wise man always lives a life of hardship. 

3. Prove that in an Aristotelian Sorites only the last prem- 
ise can be negative, and only the first particular. 



OTHER FORMS OF CATEGORICAL ARGUMENT 339 

4. Construct an Aristotelian Sorites with a particular 
negative conclusion. 

5. Prove that in a Goclenian Sorites only the last premise 
can be particular and only the first negative. 

6. Construct a Goclenian Sorites with a particular negative 
conclusion. 

7. Give one example of each class of Epicheirema. 



CHAPTER XII 

DISJUNCTIVE AND HYPOTHETICAL PROPOSITIONS AND 
ARGUMENTS 

The Disjunctive Proposition. We have already- 
distinguished the various types of logical proposi- 
tion, and discussed their relation to each other. We 
have seen that in the categorical proposition P is 
affirmed or denied of S simply. The disjunctive 
proposition, on the other hand, is the expression of 
an alternative predication. In the disjunctive prop- 
osition, the character of S seems to waver between 
a number of alternative possibilities, P or Q or M, 
and we are not able to determine which of these 
really, or for our purpose, belongs to S. 'S is either 
P, or Q, or M,' is a typical disjunctive proposition. 

Before proceedings to the discussion of the dis- 
junctive syllogism, there are several questions about 
the disjunctive proposition which require attention. 
And, first, we may note that the alternatives which 
form the predicates of such a proposition, are not 
any alternatives, but are usually alternatives that 
have something in common. We have met the con- 
verse of this statement in the chapter on division, 
where we saw that the species of a genus were to be 
understood as a series of alternatives which had a 
common nature. What we mean to express in our 
disjunctive propositions, is, therefore, not unfa- 
miliar ; and the formal statement 'S is either P or Q 

(340) 



PROPOSITIONS AND ARGUMENTS 341 

or M' may be interpreted to mean that P and Q and 
M are predicates which are, or may be, contained 
under the wider predicate R which can be asserted 
of S. For example, 'He is either a lawyer, a doctor, 
a teacher, or a clergyman,' may be expressed in the 
simpler statement, 'He is a member of a learned pro- 
fession.' The alternatives of disjunctive proposi- 
tions are usually of this class, and fall within a 
single domain or universe of discourse. They con- 
form, as do all other statements, to the limitations 
of relevant assertion. But whether every instance 
of alternative predication is actually thought of in 
its relation to a limiting universe is what we cannot 
affirm. All we hold is that logical alternatives imply 
a common basis, and that it is this common basis 
that gives to disjunction its distinctive meaning. 

Second, the question whether the alternatives of 
a disjunction should be treated as mutually exclusive 
or not has aroused a good deal of discussion, and 
there seems to be no simple answer to it. The 
meaning of the question may be made plain if we 
give it a formal expression. When it is said that 
'S is either P or Q or M,' is it necessarily implied 
that S cannot be both P and Q and M? There can 
be no doubt that in a great many instances the alter- 
native predicates do, as a matter of fact, exclude 
each other. For example, we may say that 'Plato 
was born in either 429 or 427 B. C About the in- 
surrection in Mexico we may say, 'It will either suc- 
ceed or be crushed.' Some logicians maintain that 
this is the only sense in which disjunctive predica- 



342 A TEXT-BOOK OF LOGIC 

tion can be understood in logic, and that the in- 
stances in which this does not occur are due, as 
Bradley says, to "our slovenly habits of expression 
and thought," and are "no real evidence against the 
exclusive character of disj unction." On the other 
hand, attention may be called to the fact that we 
do express our meanings in disjunctive forms which 
cannot or need not be interpreted in this exclusive 
manner. For example, ' He is either a fool or a 
knave' may mean that he is the one or the other, 
but it is quite possible for a knave to be a fool, and 
a fool, a knave. In such cases as this, where the 
truth-import and the statement-import are not neces- 
sarily the same, we are following the line of least 
error if we choose the less determinate meaning, in 
the absence of any indication that the more deter- 
minate meaning is the one intended. What the 
statement 'S is either P or Q or M,' therefore, means 
is that S cannot be neither P nor Q nor M ; it must 
be one, and, unless otherwise indicated, it may be 
more than one. We must be guided in our interpre- 
tation, not by the form of the proposition, but by the 
nature of its subject-matter. 

Thirdi the series of alternatives that constitute 
the predicates of disjunctive propositions must be 
exhaustive. That is, they must determine com- 
pletely the alternative possibilities in the given in- 
stance. If we say The water is either hot or cold,' 
the statement is misleading, if we assume that 
all the alternatives of the disjunction are ex- 
plicitly stated. But if we say The water is either 



PROPOSITIONS AND ARGUMENTS 343 

hot or cold or of some mean temperature,' the state- 
ment is true, and, in principle, exhaustive. It would 
seem, therefore, that to secure an exhaustive enu- 
meration of alternatives were more fundamentally 
important than to make them exclusive ; and in any 
case we can say that the latter is sometimes im- 
possible where the former presents no particular 
difficulty. 

The Nature and Classes of the Disjunctive Syllo- 
gism. The syllogism whose major premise is a dis- 
junctive proposition is called a disjunctive syllo- 
gism. The significance of such a syllogism consists 
in the fact that conclusions may be inferred from 
premises that are indeterminate in content; or, 
that the truth of any proposition may rest upon a 
number of conditions, one or more of which may be 
undetermined in character. 

We may distinguish two classes of disjunctive 
argument, according as the nature of the subject 
of the disjunctive major premise requires two, or 
more than two, terms to state exhaustively the alter- 
native possibilities. If the major premise of a dis- 
junctive argument has two alternatives in its pred- 
icate, the argument is called a simple disjunctive 
syllogism; if the predicate term of such an argu- 
ment presents more than two alternatives, the argu- 
ment is called mixed. The reason for this distinc- 
tion is that the character of the other two proposi- 
tions of the syllogism is affected by the consider- 
ations to which we have adverted. For in such 
arguments as we are at present concerned with, it 



344 A TEXT-BOOK OF LOGIC 

is evident that we can only affirm or deny one or 
more of the alternatives presented by the major 
premise, such affirmation or denial giving us the 
minor premise; and deny or affirm the remaining 
alternative, or alternatives, such denial or affirma- 
tion giving us the conclusion of the syllogism. Thus, 
the general rule to which disjunctive arguments 
must conform is that to affirm or deny one or more 
of the members of a series of alternatives is to deny 
or affirm the remaining member or members. Now 
if the disjunctive major premise presents only a 
pair of alternatives, the minor premise and con- 
clusion of the syllogism are both categorical prop- 
ositions; there is, in other words, only one disjunc- 
tive premise, and that the major. Such an argu- 
ment is called a simple disjunctive syllogism. If, 
on the other hand, there are more than two alter- 
natives in the disjunctive major premise, one, or 
both, of the other propositions of the syllogism must 
be disjunctive also. In such a case, we call the argu- 
ment a mixed disjunctive syllogism. 

The Moods of the Disjunctive Syllogism. Each 
class of disjunctive argument has two moods, de- 
pending upon whether the minor premise affirms or 
denies one or more of the alternatives presented by 
the major premise. The names of these moods, 
like those that we shall meet with in our study of the 
hypothetical syllogism, are derived from the Latin 
words which denote the quality of the propositions 
which constitute the minor premise and conclusion 
respectively. For example, if the minor premise is 






PROPOSITIONS AND ARGUMENTS 



345 



negative, and the conclusion is affirmative, the mood 
of the syllogism is called the Modus Tollendo Ponens, 
that is, the mood which by denying affirms. If, on 
the other hand, the minor premise is affirmative, 
and the conclusion is negative, the mood is called 
the Modus Ponendo Tollens, that is, the mood which 
by affirming denies. These statements will be 
understood if read in connection with the formulae 
for the two classes of disjunctive syllogism in each 
of these moods which follow : 



MOOD 



DISJUNCTIVE SYLLOGISM 



SIMPLE 



MIXED 



A is either B or C. 
Ponendo Tollens A ig not a 



A is either B or C or D. 

A is B. 

A is not either C or D. 



Modus 
Tollendo Ponens 



A is either B or C. 
A is not B. 
A is C. 



A is either B or C or D. 

A is not B. 

A is either C or D. 



The Validity of Disjunctive Arguments. A fur- 
ther question relates to the validity of these moods. 
We have seen that disjunctive propositions are 
required to state their alternatives exhaustively, 
that is, to enumerate alternately all the possibilities 
presented by the subject-matter under consideration. 
We have also seen that in some cases the alternatives 
are at the same time exclusive, that is, incompat- 
ible. Thus, 'A is either B or'C may mean (1) 'A 
is either B or C, but not statedly both;' or it may 
mean (2) 'A is either B or C, but statedly not both/ 



346 A TEXT-BOOK OF LOGIC 

that is, the equivalent of 'A is either B or else C 
Now in whichever way we understand the disjunc- 
tive proposition, an argument based upon it is valid 
in Modus Tollendo Ponens, because all disjunctive 
arguments imply the presence in the subject of one 
or more of the alternatives specified in the predicate 
of the major premise. That is to say, the subject 
cannot be neither of the predicated alternatives. 
The meaning of the subject professedly is to be 
found within the number of enumerated predicates. 
Hence, whether the predicates are exclusive or not, 
to deny one or more of a subject is to bring the 
subject nearer to one or more of the remaining 
predicates. That is, the Modus Tollendo Ponens em- 
phasises the exhaustive character of the disjunctive 
major. On the other hand, the Modus Ponendo Tol- 
lens is valid only when an exclusive reading of the 
major is understood. For example, when we say 
of any one that 'He is a fool or a knave/ we cannot 
infer that because 'He is a fool,' that 'He is not a 
knave/ unless it is distinctly understood that the 
individual case precludes the possibility of him being 
both. Thus, if we wish to state this meaning unam- 
biguously, we should have to say 'He is either a fool 
or else a knave/ thereby implying that he is not 
both together. When, therefore, the disjunctive 
major takes the form of 'statedly not both or all the 
predicates/ the Modus Ponendo Tollens is a valid 
mood for disjunctive arguments. This mood empha- 
sises the exclusive character of the disjunctive 
major. 



PROPOSITIONS AND ARGUMENTS 347 

The Hypothetical Proposition. Any proposition 
which states a connection between two possibilities 
is hpyothetical. For example, 'If water is heated at 
standard pressure, it will boil at 100° C There are 
two characteristics of a hypothetical proposition to 
which attention should be given. The first is that 
it is the form of statement in which we express our 
judgments when the material of these judgments is 
possible, not actual. This does not mean that the 
material dealt with may not be actual, it means only 
that we are not concerned with it as existing, but 
with the situations in which it is possible for it to 
exist. Thus, to take the judgment which is ex- 
pressed in the proposition 'If eggs are scarce, they 
will be dear.' In this proposition we are not assert- 
ing that 'eggs are scarce,' nor are we affirming that 
'they are dear;' we are merely stating that 'when- 
ever eggs are scarce, they are at the same time 
dear.' In other words, we are stating a connection 
between 'it is possible for eggs to be scarce,' and 
'it is possible for them to be dear.' 

The second characteristic of hypothetical prop- 
ositions relates to the kind of connection that they 
affirm. This may be brought out if we regard the 
judgments underlying hypothetical statements to be 
concerned with the development of the consequences 
that follow from a supposition. What leads to the 
erection of a supposition is, doubtless, some feature 
of an actually existing situation which cannot be 
brought under direct observation; but the supposi- 
tion itself is not part of the situation in the same 



348 A TEXT-BOOK OF LOGIC 

sense that the feature itself is. Any supposition is a 
suggestion which is based upon a wider range of ex- 
perience than the circumstances which calls it forth, 
and we fall back upon this broader experience to 
guide us in dealing with a situation that is proble- 
matical. Now problematic situations can be de- 
veloped only in a series of possibilities, and possi- 
bilities are expressed in hypothetical propositions: 
'If A is B, it is C The part of the hypothetical 
proposition which states the supposition or condition 
is called the antecedent, the part which states the 
result of the supposition is called the consequent. 
The connection which is thus affirmed by hypothet- 
ical propositions is a relation of dependence between 
antecedent and consequent, such that the truth of 
the consequent follows necessarily upon the estab- 
lishment of the antecedent. The hypothetical 
proposition thus states a rule under which we may 
bring for testing any fact or situation about which 
we are at all doubtful. It should be observed that 
it is the nature of the thought expressed, and not 
the form of the expression that constitutes any 
proposition hypothetical. While usually we intro- 
duce hypothetical statements with 'if,' they may be 
prefaced by 'granted that,' 'suppose that,' 'allowing 
that,' 'whenever,' 'wherever;' and sometimes there 
is no verbal sign to indicate that our thought is 
hypothetical, as, for example, 'Trespassers will be 
prosecuted,' 'Deserters will be shot on sight,' etc. 

The Hypothetical Syllogism. Any syllogism in 
which the major premise is a hypothetical proposi- 



PROPOSITIONS AND ARGUMENTS 349 

tion is called a hypothetical syllogism. In hypothet- 
ical arguments the minor premise and the conclusion 
are both categorical propositions. Now since the 
major premise states a connection between two 
possibilities, the minor premise must state some- 
thing about one or other of these possibilities cate- 
gorically if there is to be an inference. The only 
things that can be stated are that either of the pos- 
sibilities has or has not been verified. Theoretically, 
this would give four kinds of hypothetical syllo- 
gism, the minor premises of which would affirm and 
deny separately the antecedent and consequent of 
the major premise. Two of these, however, fail to 
give the proper basis for an inference, namely, when 
the minor premise denies the antecedent, and when 
it affirms the consequent. The reason for the fail- 
ure is that we are in each case required to go be- 
yond what is contained in the major premise. For 
example, when we say 'If A is B, it is C/ we are not 
to be understood to mean that the only condition of 
'A being (7 is that 'A is B.' We said above, for in- 
stance, that 'If eggs are scarce, they are dear;' but, 
of course, they may be dear for other reasons as 
well, — a corner on the market by the cold storage 
interests, for example. Hence, if we were to deny 
the antecedent of this proposition, 'Eggs are not 
scarce/ and use this as a minor premise, we could 
not infer that 'they are not dear.' The antecedent 
of a hypothetical proposition states a condition, but 
does not offer itself as the sole condition of the 
truth of the consequent. If, on the other hand, 



350 A TEXT-BOOK OF LOGIC 

we were to affirm the consequent, 'Eggs are dear/ 
we cannot infer that 'they are scarce,' and the rea- 
son is the same. The forms of the syllogism are 
reduced, therefore, to two, in one of which the 
minor premise affirms the antecedent of the major, 
and in the other the minor premise denies the con- 
sequent of the major. In reference to these forms 
of the syllogism, we may state the general rule of 
hypothetical arguments as follows : When two pos- 
sibilities are related as antecedent and consequent, 
the truth of the consequent follows from the truth 
of the antecedent, and the falsity of the antecedent 
follows from the falsity of the consequent. 

The Moods of the Hypothetical Syllogism, Corre- 
sponding to these two forms of hypothetical argu- 
ment we may distinguish two moods of the syllo- 
gism. There is first the argument in which the 
minor premise affirms the antecedent of the major 
premise, — the Modus Ponens ; and, second, the 
argument in which the minor premise, denies the 
consequent of the major premise, — the Modus Tol- 
lens. 

The antecedent and consequent of the major 
premise of any hypothetical syllogism may be either 
affirmative or negative. In each of the two moods, 
therefore, we may distinguish four forms of hypo- 
thetical argument as follows: (1) the antecedent 
and consequent of the major premise may both be 
affirmative; (2) the antecedent may be affirma- 
tive, and the consequent negative; (3) the antece- 
dent may be negative, and the consequent affirm- 



PROPOSITIONS AND ARGUMENTS 351 

ative; (4) both antecedent and consequent may be 
negative. It will be evident that arguments in these 
moods will have sometimes an affirmative and some- 
times a negative proposition in the minor premise, 
and the same will be true of the conclusion. The 
names of the several forms of the moods of hypo- 
thetical syllogisms, like those of the disjunctive syl- 
logism, are derived from the Latin words which de- 
scribe the quality of the propositions which consti- 
tute the minor premise and the conclusion. We 
shall briefly characterise each mood and give exam- 
ples and formula? for the different forms of the two 
moods. 

i. Modus Ponens, — the mood in which the minor 
premise affirms the antecedent of the major premise, 
and the conclusion affirms the consequent. Argu- 
ments in this mood are said to be Constructive. 
The validity of arguments in this mood is based 
upon the fact that we are bound to accept whatever 
follows from any data we have accepted. If, for 
example, we accept as a possibility a fall in temper- 
ature, we are bound to accept whatever is condi- 
tioned upon this possibility, say, colder weather. 
We may, therefore, construct a hypothetical argu- 
ment in this mood as follows: 

A fall in temperature means colder weather. 
The temperature is falling. 
Therefore, the weather will be colder. 



352 A TEXT-BOOK OF LOGIC 

The different forms of the Modus Ponens are 
given here with illustrations of each form. 

(i) Modus Ponendo Ponens, — the mood which by 
affirming affirms. 

If A is B, it is C. If any county increases in wealth, 
it increases in power; 

A is B, The United States is increasing in 

wealth, 

A is C, Therefore, the United States is in- 

creasing in power. 

(2) Modus Ponendo Tollens, — the mood which by 

affirming denies. 

If A is B, it is-not C. If any import duty is imposed 
simply for revenue purposes, that 
duty is not protective; 

A is B. The English import duties are im- 

posed simply for revenue purposes; 

A is-not C. Therefore, they are not protective. 

(3) Modus Tollendo Ponens, — the mood which by 

denying affirms. 
If A is not B, it is C. If any swan is not white, it is 

black ; 
A is-not B. Australian swans are not white, 
A is C. Therefore, they are black. 

(4) Modus Tollendo Tollens, — the mood which by 

denying denies. 
If A is-not B, it is-not C. If any war is not defensive, 
it is not just; 



PROPOSITIONS AND ARGUMENTS 353 

A is-not B. The wars waged by Napoleon the 

Great were not defensive, 
A is-not C. Therefore, they were not just. 

2. Modus Tollens, — the mood in which the minor 
premise denies the consequent of the major premise, 
and the conclusion denies the antecedent. Argu- 
ments in this mood are said to be Destructive. The 
validity of arguments in this mood follows from the 
relations expressed by the major premise. For if 
B follows of necessity from the existence of A, — 
'If A then B,' — the failure of B to appear must mean 
the absence or non-existence of A. An illustration 
of an argument in this mood is : 

If no men were mad, asylums would be useless, 
Asylums are-not useless, 
Therefore, some men are mad. 
The different forms of the Modus Tollens are 
given here with illustrations of each form. 

( i ) Modus Tollendo Tollens, — the mood which by 
denying denies. 

If A is B, it is C. If any country is civilised, it has 
a population amongst whom educa- 
tion is general; 

A is-not C. The people of Russia are not gener- 
ally educated; 

A is-not B. Therefore, Russia is not a civilised 
country. 

23 



354 A TEXT-BOOK OF LOGIC 

(2) Modus Ponendo Tollens, — The mood which by 

affirming denies. 
If A is B, it is not C. If any social institution is 

justifiable, it oppresses no class of 

the community ; 
A is C. Slavery does oppress a class of the 

community, 
A is-not B. Therefore, it is not justifiable. 

(3) Modus Tollendo Ponens, — the mood which by 

denying affirms. 
If A is-not B, it is C. If any railroad is not required 

in the district through which it runs, 

it is a financial failure; 
A is-not C. The great American lines are not 

financial failures, 
A is B. Therefore, they are required in the 

districts through which they run. 

(4) Modus Ponendo Ponens, — the mood which by 

affirming affirms. 

If A is-not B, it is-not C. If any country has no 
capital invested abroad, its imports 
will not exceed its exports; 

A is C. England's imports do exceed her ex- 

ports, 

A is B. Therefore, England has capital in- 

vested abroad. 

Dilemmas. We come now to the study of dilem- 
mas, a class of arguments which combines in various 
ways characteristics of the three kinds of proposi- 



PROPOSITIONS AND ARGUMENTS 355 

tion already studied, the categorical, the disjunctive, 
and the hypothetical. The peculiar feature of a 
dilemmatic argument is that it presents a choice 
between two alternatives. When used for rhetor- 
ical purposes these alternatives are of such a kind 
that, whilst one of them must be accepted, both lead 
to disagreeable results. To force by argument the 
acceptance of one or other of a pair of alternatives 
is the chief function of the dilemma, and as the re- 
sult of such an argument an opponent is said 'to be 
on the horns of a dilemma.' Arguments in which 
the choice rests among three alternatives are not 
dilemmas in the strict definition of the term, but 
trilemmas, just as those which force a choice among 
four alternatives are tetralemmas. The principles 
of all these arguments, however, are the same,, and 
it will be sufficient to study them in connection with 
the simplest forms, — the dilemmas. 

The dilemma may be defined as a syllogism with 
a compound hypothetical major premise and a dis- 
junctive minor. By a compound hypothetical prop- 
osition is meant one in which there is a plurality 
of terms in either the antecedent or consequent, or 
in both. The simplest form of hypothetical prop- 
osition, we have seen, is 'If A is B, it is (V Such 
a proposition may become compound by adding 
terms to antecedent and consequent. 'If A is B, it 
is C or D,' is a compound hypothetical proposition, 
and we must understand it to mean 'If A is B, it is 
C and 'If A is B, it is also D.' That is to say, there 
is no true disjunction in this case, but only an ab- 



356 A TEXT-BOOK OF LOGIC 

breviated expression of two simple hypothetical 
propositions. The same remarks hold good also of 
the other forms that compound hypothetical prop- 
ositions may assume; for example of, 'If A is B or 
C, it is D ;' 'If A is B or C, it is D or E.' Proposi- 
tions of this type form the major premises of dilem- 
matic arguments. The reason why propositions of 
this type constitute the major premise of dilemmatic 
arguments is quite clear. For if the dilemma is 
thought of as an argument which leads to a con- 
clusion through the affirmation or denial of alter- 
natives in the minor premise, the major premise of 
such an argument must provide the basis for the 
alternatives affirmed or denied in the minor premise, 
and this it can do only when there is a plurality of 
terms in the antecedent, consequent, or both, of 
the major premise. In view of these more general 
statements, the structure of the dilemma will be 
evident from the following analysis : 

1. The major premise is a compound hypothet- 
ical proposition 

a. with a one-term antecedent and a two- 
term consequent, 

b. or with a two-term antecedent and a one- 
term consequent, 

c. or with a two-term antecedent and a two- 
term consequent. 

2. The minor premise is a disjunctive proposi- 
tion. 



PROPOSITIONS AND ARGUMENTS 357 

3. The conclusion is 

a. either a categorical proposition, when the 
major premise has a one-term antecedent 
or consequent. 

b. or a disjunctive proposition, when the 
major premise has a two-term antecedent 
and consequent. 

Classes of Dilemma. Dilemmas, which are gov- 
erned by the laws of the hypothetical syllogism, are 
of two kinds, — Constructive and Destructive. A 
dilemma is said to be constructive when the minor 
premise affirms the antecedent of the major, and to 
be destructive when it denies the consequent of the 
major disjunctively. Within each of these kinds, 
there are two forms, — Simple and Complex. A 
dilemma is said to be simple when its major premise 
has a single antecedent or consequent, and it is said 
to be complex when both the antecedent and conse- 
quent of the major premise contain two terms. We 
proceed now to the study of each of these kinds of 
dilemma, and to an examination of the forms that 
they may assume. 

i. Constructive Dilemma, — an argument which 
proceeds from the acceptance of the antecedent to 
the acceptance of the consequent of the major 
premise. 

(i) Simple Constructive Dilemma, — an argument 
whose minor premise affirms disjunctively the ante- 
cedent of the major, and whose conclusion categor- 
ically affirms the consequent. 



358 A TEXT-BOOK OF LOGIC 

If either A or B, then C. If a science furnishes use- 
ful facts, or if the study of it exer- 
cises the reasoning powers, it is 
worthy of being cultivated; 
Either A or B. But either a science furnishes useful 
facts, or its study exercises the rea- 
soning powers; 
Therefore, C. Therefore, it is worthy of being cul- 
tivated. 
(2) Complex Constructive Dilemma, — an argu- 
ment whose minor premise disjunctively affirms the 
antecedent, and whose conclusion disjunctively 
affirms the consequent. 

If A then C, and if B then D. If Aeschines joined 
in the public rejoicings, he is incon- 
sistent; if he did not he is unpa- 
triotic ; 
Either A or B. But either he did or did not; 
Therefore, either C or D. Therefore, he is either 
inconsistent or unpatriotic. 
2. Destructive Dilemma, — an argument which 
proceeds from the denial of the consequent to the 
denial of the antecedent. 

(1) Simple Destructive Dilemma, — an argument 
whose minor premise denies disjunctively the conse- 
quent of the major, and whose conclusion categor- 
ically denies the antecedent. 

If A, then both B and C. If table-rappers are to be 
trusted, the departed are spirits, and 
they also exert mechanical energy ; 



PROPOSITIONS AND ARGUMENTS 359 

Either not B or not C. But either the departed are 
not spirits or they do not exert me- 
chanical energy; 

Therefore, not A. Therefore, table-rappers are not 
to be trusted. 

(2) Complex Destructive Dilemma, — a n argu- 
ment whose minor premise disjunctively denies the 
consequent of the major, and whose conclusion dis- 
junctively denies the antecedent. 
If A then C, and if B then D. If the industry of the 
United States is well organised, there 
is work for every efficient labourer 
who seeks it, and if all labourers are 
industrious, they will seek work. 
Either not C or not D. But either some labourers 
cannot get work, or they will not 
seek it; 
Therefore, either not A or not B. Therefore, either 
the industry of the United States is 
not well organised, or some labourers 
are not industrious. 
The Validity of the Dilemma. The logical value 
of dilemmatic arguments has frequently been called 
in question. Thus Jevons says, "Dilemmatic argu- 
ments are more often fallacious than not." It may, 
therefore, serve to emphasise the character of these 
arguments if we indicate where their use may in- 
volve us in error. The fallacious character of a 
dilemma must foe sought either in the major or in 
the minor premise. In the major premise, the ante- 



360 A TEXT-BOOK OF LOGIC 

cedent or consequent may not express possibilities, 
in which case the error will be easily detected; or 
the asserted connection between them may be false, 
in which case the error is likely to be obvious. For 
example, if we do not admit that 'A is B' and 'A is C 
are possibilities, then we are not likely to admit that 
If A is B, it is C is a possible premise of an argu- 
ment. But if we admit both as possibilities, we may 
not admit that the one follows as a consequence from 
the other, and this will preclude 'If A is B, it is C 
from figuring as the major premise of an argument. 
We thus see that before we can accept a compound 
hypothetical proposition as the major premise of a 
syllogism, we are required to admit that both ante- 
cedent and consequence are possibilities, and that 
they are related to each other as condition and con- 
ditioned. For example, it is possible for a triangle 
to be equilateral, it is also possible for a triangle to 
be equiangular, but in this case wherever one of 
these possibilities is realised the other is also found, 
the one is conditioned by the other. These are the 
facts that we express in the statement, 'If a triangle 
is equilateral, it is equiangular.' 

Error arises most frequently, however, in the 
minor premise. The reason for this is that the 
alternatives may not be either exhaustive or ex- 
clusive. The difficulty of getting a dichotomous 
alternative which is exhaustive is due partly to the 
complex nature of the subjects of discourse, and 
partly to the fact that the major premise of thec Q 
arguments is concerned only with the relation of 



Propositions and arguments 361 

antecedents and consequence, and not with disjunc- 
tive relations. The proposition If A is B, it is C 
or D' means, as we have seen, that 'A is B' is the 
condition of both 'A is C and 'A is D.' When, 
therefore, we affirm these two disjunctively in 
the minor premise of an argument, we must do so 
on other grounds than that they are antecedents or 
consequent of a compound hypothetical major pre- 
mise. Hence, to quote Jevons, "if we were to argue 
that 'if a pupil is fond of learning, he needs no 
stimulus, and that if he dislikes learning, no stimulus 
will be of any avail; but as he is either fond of 
learning or dislikes it, a stimulus is either needless 
or of no avail/ we evidently assume improperly the 
disjunctive minor premise. Fondness and dislike 
are not the only two possible alternatives, for there 
may be some who are neither fond of learning nor 
dislike it, and to these a stimulus in the shape of 
rewards may be desirable. Almost anything can be 
proved if we are allowed to pick out two of the 
possible alternatives which are in our favor, and 

argue from these alone." 

< 

REFERENCES. 
H. A. Aikins, The Principles of Logic, Ch. XVII. 
B. Bosanquet, The Essentials of Logic, Lecture VI. 
J. E. Creighton, An Introductory Logic, 3d Edition, Ch. XI. 
J. G. Hibben, Logic, Deductive and Inductive, Part I., Ch. 

XVI. 
W. S. Jevons, Elementary Lessons in Logic, Lesson XIX. 
J. N. Keynes, Formal Logic, 2d Edition, Part III., Chs. VII., 

VIII. 



362 A TEXT-BOOK OF LOGIC 

S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
tion, Ch. VII. 

W. Minto, Logic, Inductive and Deductive, Book I., Part IV., 
Ch. VII. 

C. Read, Logic, Deductive and Inductive, 3d Edition, Ch. XII. 

W. J. Taylor, Elementary Logic, Ch. XII. 

ADVANCED 

B. Bosanquet, Logic, Chs. VI., VIII. 

F. H. Bradley, The Principles of Logic, Book I., Chs. II., IV. 
W. R. B. Gibson, The Problem of Logic, Chs. XXX., XXXI., 

XXXII. 
H. W. B. Joseph, An Introduction to Logic, Ch. XV. 
H. Lotze, Logic, Book I., Ch. II., B, C. 
F. C. S. Schiller, Formal Logic, Ch. XVII. 

C. Sigwart, Logic, Vol. I., Part I., Ch. VII. 
J. Venn, Empirical Logic, Ch. X. 

J. Welton, A Manual of Logic, Vol. I., Book IV., Ch. V. 

QUESTIONS 

1. What kind of predication underlies the disjunctive prop- 
osition? 

2. What relation has disjunctive assertion to the universe 
of discourse? 

3. Discuss the question whether the alternatives of a log- 
ical disjunction are exclusive. 

4. "The alternatives of a disjunctive proposition must be 
exhaustive." Explain. 

5. What are the characteristics and significance of a dis- 
tinctive syllogism? 

6. Discuss and illustrate the main classes of disjunctive 
syllogism. 

7. Why do we distinguish classes of disjunctive argument? 

8. What are the functions of the minor premise and con- 
clusion of a disjunctive syllogism? 

9. In what Moods may a disjunctive syllogism be stated? 



PROPOSITIONS AND ARGUMENTS 363 

10. How will your interpretation of 'A is either B or C be 
affected, if the alternatives are understood to be ex- 
clusive, and if they are understood to be not necessarily 
exclusive? 

11. Why is the disjunctive syllogism in Modus Tollendo 
Ponens valid whichever view of alternation we take? 

12. Why is a disjunctive syllogism in Modus Ponendo Tol- 
lens valid only if we give an exclusive reading of the 
major premise? 

13. What is a hypothetical proposition? 

14. Name and state the difference between the main classes 
of hypothetical proposition. 

15. What is meant by saying that the material of the judg- 
ments which are expressed in hypothetical propositions 
is possible not actual? 

16. "Hypothetical propositions state the connection of a sup- 
position and what follows from it." Explain. 

17. Into what two parts may a hypothetical proposition be 
analysed? 

18. What are the characteristics of a hypothetical syllogism? 

19. Why does the denial of the antecedents, and the affir- 
mation of the consequents of the major premise of a 
hypothetical syllogism make it impossible to state any 
valid conclusion? 

20. What are the rules of valid inference for hypothetical 
arguments ? 

21. In what Moods may a hypothetical argument be stated 
validly? 

22. In what Mood is a hypothetical argument constructive? 

23. Describe and illustrate the Modus Ponens, and state 
why hypothetical arguments in this Mood are valid. 

24. State and illustrate the different forms of the Modus 
Ponens. 

25. In what Mood is a hypothetical argument destructive? 

26. Describe and illustrate the Modus Tollens, and state 
why hypothetical arguments in this Mood are valid. 



364 A TEXT-BOOK OF LOGIC 

27. State and illustrate the different forms of the Modus 
Tollens. 

28. What is it to be 'on the horns of dilemma'? 

29. How do dilemmas, trilemmas and tetralemmas differ 
from one another? 

30. Define a dilemma. 

31. What are the various theoretically possible forms of 
dilemma? 

32. What is a constructive dilemma? 

33. Describe and illustrate the various forms of constructive 
dilemma. 

34. What is a constructive dilemma? 

35. Describe and illustrate the various forms of destructive 
dilemma. 

36. What must we admit with respect to the major premise 
of a dilemma before it can serve as the basis of a valid 
conclusion? 

37. What sources of possible error are found in the minor 
premise of a dilemmatic argument? 

EXERCISES. 

1. Write three disjunctive propositions in which the alter- 
natives are exhaustive and exclusive. 

2. Construct on the basis of your answer to the previous 
question three arguments in Modus Ponens. 

3. Construct three disjunctive syllogisms in Modus Tollens. 

4. Write three hypothetical propositions, only one of which 
may be introduced by 'if.' 

5. State the nature and Mood of the following arguments, 
and examine their validity: 

(1) If the study of logic furnishes the mind with a mul- 
titude of useful facts, like other sciences, it would 
deserve to be cultivated ; but it does not furnish the 
mind with a multitude of useful facts; therefore, 
it does not deserve cultivation. 



PROPOSITIONS AND ARGUMENTS 365 

(2) Mars must have warmth sufficient for protoplasmis 
metabolism, if life exists there; but life is not pos- 
sible there, since the planet has not sufficient 
warmth for the purpose named. 
6. What are the nature and validity of the following argu- 
ments : 

(1) If you say what is just, men will hate you; and if 
you say what is unjust, the gods will hate you. 
you must say one or the other. Therefore, you 
you will in either case be hated. 

(2) If he were clever, he would see his mistake; and if 
he were candid he would acknowledge it. But either 
he does not see his mistake, or will not acknowl- 
edge it. Therefore, he is either not clever or not 
candid. 



CHAPTER XIII 

INDUCTION AND METHODS PRELIMINARY TO INDUCTION 

General Statement of the Problem. In the fore- 
going chapters, knowledge was said to have two 
sides, from one of which it is seen to be almost 
wholly identified with what we call truth, and from 
the other it appears to be almost wholly concerned 
with what are called facts. On whichever of these 
two sides of knowledge we may chance to look, we 
are exposed to the danger of neglecting the other, 
and thus of forgetting that the distinction of truth 
and fact is only relative. If we say that the dis- 
tinction is one that concerns the contrast that is 
ordinarily made between our thoughts-about-objects 
(truth) and the objects-thought-about (facts), it 
will not require a great deal of analysis to show that 
truth and fact are not two separate things, but two 
ways of looking at the same thing; and conse- 
quently, that if we try to separate them, in order 
to give exclusive existence to either, we can get rid 
of the one only by losing our grasp also upon the 
other. Thoughts without things are empty, and 
things without thoughts are meaningless. 

Our previous discussions have led us to lay em- 
phasis mainly upon the various ways in which our 
thoughts-about-things are capable of constant im- 
provement and expansion. We may be said to have 
taken for granted the existence of truth, and our 

(366) 



INDUCTION AND METHODS 367 

problem was to study the methods by which one 
truth is or may be connected with another; to ex- 
pound in an elementary way the systematic char- 
acter of truth. From this point of view, the syllo- 
gism appeared as an instrument for bringing par- 
ticular truths under general rules ; it enabled us to 
see what were the conditions of the- connection of 
one truth with another. In definition and classifi- 
cation we were studying how to make truth more 
explicit, to rid it of ambiguity, and to bring out 
other important features. In brief, we have been 
studying the judgment as the distinctive element 
in knowledge, and expounding the relations that 
judgments may sustain to each other. 

In the present chapter, we turn to another group 
of problems that is suggested when attention is 
given to facts rather than, truths. Now about 
facts, the logical consideration of which is commonly 
referred to as induction, we are primarily interested 
to know how facts are constituted; what we mean 
by fact, and what conditions fact must satisfy if 
the world of fact, like the world of truth, is to be- 
come systematic. Broadly stated, the problem of 
induction is an inquiry into the process by which, 
when we start with particular facts, universally 
valid statements about reality can be established. 

What is Meant by Fact. There are several fea- 
tures of this statement of the problem of induction 
that need elucidation. And first, what precisely do 
we mean by fact? The word is used in a narrower 
and a broader way. It is used in a narrow sense 



368 A TEXT-BOOK OF LOGIC 

to indicate the objects of our knowledge of the mate- 
rial world, such as trees, mountains, railroads, 
streets, houses, etc. In the broader sense, it is used 
to indicate any object of knowledge, whether mate- 
rial or not, of which we may be said to have knowl- 
edge. Used in this latter way, a sensation, an idea, 
a purpose, an emotion, when they are made the 
objects of knowledge, would also be facts. If we 
compare these two uses of the word, we shall see 
that a single meaning underlies both; they differ 
only in the range of its application. For both, a 
fact is any object of which we are said to possess 
knowledge. 

We may observe further that by knowledge as a 
conscious process is meant a judging process; hence, 
we may say that whatever is the object of a judging 
process is a fact, and nothing else is. What a judg- 
ing process is has been explained in earlier chapters, 
and it is important here merely to remark that 
it is only when objects are made the subjects of 
judgments, and are qualified in distinctive ways, 
that they can be spoken of as facts. Facts, then, 
are objects that have been qualified by our thoughts 
about them. Now there are a number of ways in 
which facts are qualified by our thoughts about 
them ; for instance, we think about them as possess- 
ing certain qualities, as being in a certain place, as 
continuing to exist for a certain length of time, as 
related to other objects in numerous ways. The 
important words in these instances are quality, 



INDUCTION AND METHODS 369 

place, time, relation. In logic these are called cate- 
gories. 

The problem of the categories is much too diffi- 
cult a subject for discussion in an elementary book 
of logic, but the student is required to understand 
at least what the word means and how it is used. 
We may say, then, that the categories are names 
for the differences in the forms of our thought about 
things; and, because thoughts and things imply 
each other, they indicate also a distinction in the 
nature of the things about which we think. If we 
remember that etymologically category means pred- 
icate, the categories may be looked upon as a list of 
the classes of attributes that can be predicated of a 
subject in a logical proposition. Thus, if we say 
that 'Man is an animal,' the term animal tells us 
what kind of a substance man is; we are thinking 
about man under the category of substance. If, 
again, we say that The violets have a sweet odour,' 
we are thinking about violets under the category of 
quality. How many categories or generic differences 
in the forms of our thought about things there are 
is a matter that does not concern us here; the list 
varies with different writers, but Aristotle names 
ten. The point to emphasise is that the predicates 
of logical propositions can be classified under a 
number of main heads which denote the general 
forms of our thinking about things, and these forms 
of thought are called categories. Until we have 
thought the objects of consciousness under one or 

24 



370 A TEXT-BOOK OF LOGIC 

more of the categories in an act of judgment, they 
are not properly called facts; a fact is, from this 
point of view, any object of consciousness which 
has been thought under one or more of the cate- 
gories. 

Nature of Reality. Our statement of the induc- 
tive problem contains, secondly, the word reality. It 
is, we said, about reality that we seek universally 
valid judgments. What is reality? The answer to 
this question, like that of the categories, is too diffi- 
cult for an elementary discussion, and besides the 
subject itself belongs to another department of phil- 
osophy, namely, to metaphysics. But we may under- 
stand the term well enough for our present pur- 
poses, if we utilise the results of our examination 
of the meaning of fact. Broadly stated, by reality 
is meant the 'world of fact.' What such a phrase as 
that just employed is ordinarily understood to 
emphasise is that facts are not isolated, unrelated 
things ; that they are, on the contrary, connected in 
numerous ways with other facts. This is a matter 
of our ordinary every day observation and expe- 
rience. We put our hand in the fire and it is burned. 
We eat too much or eat the wrong things, and our 
bodies suffer. In the social world, we have a dis- 
agreement with one person, and the behaviour of a 
number of others toward us is affected thereby. 
The movements of the planetary bodies regulate our 
seasons, the rain fall determines the size of our 
crops. These instances are sufficient to suggest, 
what is true throughout our experience, that facts 



INDUCTION AND METHODS 371 

do not exist apart from each other, but are, so to 
speak, bound up in bundles together. Such bundles 
or groups of fact we speak of as worlds of fact. 
If we carry our observation further, it will appear 
that as individual facts are related to each other so 
these bundles of facts are connected in numerous 
ways. The combinations of these more complex 
groups we may also call worlds of fact. Thus we 
have the world of commerce, the world of conduct, 
the world of religion, the world of science. Within 
each of these worlds, the facts, although diverse, 
are generically related, — they are facts of a given 
kind. Looked at in one way, it seems as if these 
several worlds had little if anything in common, and 
that there were consequently a pluralism of such 
worlds. A little closer study has convinced some 
men, however, that we can detect a likeness between 
some of these worlds on the ground that they are 
concerned with material things, and that a likeness 
exists between still others on the ground that they 
are concerned with mental things. If this is true, 
the many worlds are reduced to two, each of which 
is very complex, and between which there is said 
to exist no similarity at all. Whether this is true 
or not we need not discuss ; it is a question that be- 
longs to the philosopher, and there does not seem to 
be any general agreement about it. The point to 
emphasise is that whether there be one or many 
worlds of fact, every one is agreed that when we 
speak about reality we are speaking about those 
worlds and the facts therein contained. When, 



372 A TEXT-BOOK OF LOGIC 

therefore, we say that the problem of induction is 
an inquiry into the processes by which, starting 
with particular facts, universally valid statements 
about reality can be established, we mean that we 
are interested in finding out the truth about these 
worlds, what are the relations between the facts 
which give these worlds their characteristic fea- 
tures, and make them the permanent realities they 
appear to be. 

Our study of this problem falls into two parts. 
In the first part, we shall consider a number of 
processes preliminary to induction, and with which 
induction frequently has been confused; in the sec- 
ond part, we shall expound the inductive process 
strictly so-called, a process, however, which we shall 
see emerging into a clearer and clearer light in our 
exposition of the first part. The present chapter is 
devoted to the former task; the next four to the 
latter. 

Induction by Simple Enumeration. A prevalent 
notion identifies induction with an examination of 
a number of instances of a given phenomenon. 
Whenever we are comparing a number of particular 
facts for the purpose of discovering in what re- 
spects they are alike, we are supposed, by those who 
hold this view, to be engaged in an inductive pro- 
cedure. In agreement with this supposition, the dis- 
tinction has been drawn between perfect and imper- 
fect induction. In the case of perfect induction, we 
are dealing with a group of facts all the members 
of which are known. Thus, we may make state- 



INDUCTION AND METHODS 373 

ments about the days of the week or the months of 
the year, and be quite sure that no instances, other 
than those we have examined, will occur to make a 
revision of our judgment necessary. We may say, 
for example, that 'All the months of the year have 
less than thirty-two days,' and 'The week consists 
of seven days.' Whenever the group of facts we are 
examining is known to be limited, we may collect 
all the instances and observe each before making 
the general statement. The enrollment of students 
in a college class is such a definitely limited group, 
and about it we may, for example, make the state- 
ment that 'None of the students in this class is over 
six feet tall.' Imperfect induction is based upon 
the same principle of counting and comparing in- 
stances, but we have no assurance that all the cases 
that have been examined are all the cases that exist, 
and, therefore, a lower degree of certainty is sup- 
posed to belong to the statements that, under these 
circumstances, we are able to make. This was the 
view of induction commonly held during the Middle 
Ages. It consists in stating that all the known in- 
stances of a given kind possess a certain attribute, 
and, therefore, that all instances of this kind will 
be found to possess the same attribute. For ex- 
ample, the Negroes of Africa for centuries had seen 
no human beings who were not black; they would, 
therefore, suppose that all human beings were black. 
For many centuries each and every crow that had 
been observed by Europeans was black; it was, 
therefore, supposed that all crows were black. In 



374 A TEXT-BOOK OF LOGIC 

both these instances the induction has been found 
to be erroneous. The fault to which every imperfect 
induction is liable is that experience is likely at some 
time to prove it wrong. 

Both of these kinds of induction have been re- 
jected by writers in the modern era, and especially 
by Bacon and Mill. Perfect induction, Mill says, is 
of no scientific value ; the conclusion is only a state- 
ment in a different form of the premises. The con- 
clusion, in other words, is merely an enumerative 
judgment, — a judgment which summarises the 
data and does not lead beyond them. In induction 
proper, we are said to go beyond what is con- 
tained in our data ; we proceed from the known par- 
ticulars to the unknown universal, from what is 
true of a given case or number of cases to what is 
true always and everywhere of all cases whatsoever. 
Jevons, on the other hand, defends perfect induc- 
tion, and in doing so states very well the value that 
we may attach to this process. He says : "If Per- 
fect Induction were no more than a process of abbre- 
viation, it is yet of great importance, and requires 
to be continually used in science and common life. 
Without it we could never make comprehensive 
statements, but should be obliged to enumerate 
every particular. . . . The fact is, that the power 
of expressing a great number of particular facts in 
a very brief space is essential to the progress of 
science. Just as the whole art of arithmetic con- 
sists in. nothing but a series of processes for abbre- 
viating addition and subtraction, and enabling us to 



INDUCTION AND METHODS 375 

deal with a great number of units in a very short 
time, so Perfect Induction is absolutely necessary 
to enable us* to deal with a great number of par- 
ticular facts in a very brief space." 

The case of imperfect induction is not in prin- 
ciple different. Imperfect induction, says Bacon, 
"proceeds by merely citing instances and is a child- 
ish affair (res puerilis) , and being without any cer- 
tain principle of inference it may be overthrown by 
a single negative instance." By a negative instance, 
Bacon means an instance which contradicts all the 
instances that previously have been examined. For 
example, a single instance of a grey crow over- 
throws the inference that all crows are black. Mill, 
referring to imperfect induction, says that "it con- 
sists in ascribing the character of general truths to 
all propositions which are true in every instance 
that we happen to know of. . . . In science it 
carries us but a little way. We are forced to begin 
with it; we must often rely on it provisionally, in 
the absence of means of more searching investiga- 
tion. But, for the accurate study of nature, we re- 
quire a surer and a more potent instrument." This 
more potent instrument is "to be found in interro- 
gating nature" by experiment, so as to discover the 
conditions under which the phenomena occur. 

The Value of Simple Enumeration. In the pre- 
ceding section, we have examined the two forms of 
induction by simple enumeration, and we have seen 
that in perfect induction all the positive instances, 
and in imperfect induction a larger or smaller num- 



376 A TEXT-BOOK OF LOGIC 

ber of the positive instances of a phenomenon are 
available for observation. The conclusion that is 
based upon a complete enumeration of the instances 
does not go beyond these instances themselves, 
whereas the conclusion that is based upon an in- 
complete enumeration is understood to apply also 
to instances that have not been examined and that 
may not be known to exist. In the former case, the 
conclusion may be described as an empirical general- 
isation; in the latter, the conclusion has the charac- 
ter of an hypothesis which is held subject to revision 
or rejection in view of our examination of other 
instances that may come to light. These descrip- 
tions serve to distinguish the scientific value of these 
two forms of simple enumeration. Perfect induc- 
tion belongs to the stage preliminary to induction, 
whilst imperfect induction must be classed among 
the steps of induction properly so-called. The lat- 
ter, we shall reserve for future consideration, and 
turn our attention immediately to the former. 

Empirical Generalisation. Induction by complete 
enumeration, which, as we said, leads to an em- 
pirical generalisation, is not entirely a simple proc- 
ess, and it suggests certain questions of importance 
for the study of induction. These questions we shall 
consider in this section. And first we should ob- 
serve that if we ask why there is any such process 
of combining in single statements a number of facts, 
why we classify at all, we may perhaps say with 
Mill, who in this follows Hume, that there is a ten- 
dency of the mind "to generalise its experience, pro- 



INDUCTION AND METHODS 377 

vided this points all in one direction." This abbre- 
viation and summation of numerous facts and expe- 
riences takes place as a measure of protection 
against being overwhelmed with the diversity of the 
events which life daily presents to each of us. It is 
not a method that is peculiar to science; it is used 
by all of us in common life. It has a practical 
value; it does, as Mill points out, facilitate our 
handling a great number of data. But because we 
cannot escape using it, and because its employment 
is so general, the method is not, therefore, altogether 
simple. It presupposes the existence of ideas, — of 
the idea, at any rate, that all the instances we ex- 
amine may possibly constitute a single class. When, 
however, we ask by virtue of what particular idea 
a number of facts constitute a class, we must re- 
member that classes, as we saw in the chapter on 
classification, are not ready made things ; there are, 
as we said, no 'natural kinds,' nor, on the other 
hand, are there any ready made ideas, except as 
those have been acquired in the course of experience, 
that can serve as principles of classification. The 
fact is that we classify on the basis of observed like- 
nesses, and the members of a class are determined 
by the kind of likenesses with respect to which 
each instance is examined. In science, the principle 
of classification is consciously entertained; in com- 
mon life, it is not brought into clear definition. In 
the latter case, we are guided by the accidental at- 
tributes of phenomena, and our generalisations 
have, as a rule, the value merely of shorthand mem- 



378 A TEXT-BOOK OF LOGIC 

oranda ; by them we are able to get back to the facts 
at any time we wish, but our understanding of the 
facts is not thereby advanced. The process is not 
for this reason without value, but its particular 
worth is likely to be obscured if we fail to observe 
its limitations. We may, therefore, repeat that 
empirical generalisations do not make any group of 
facts, for science or for common life, more intel- 
ligible; they merely group together a number of 
data, and thereby suggest that the observed mate- 
rial may be connected in some more fundamental 
way. It is because they hint at some underlying 
principle of connection that empirical generalisa- 
tions have a place in the method of scientific inves- 
tigation. 

Colligation of Facts. A method of dealing with 
facts which emphasises more directly the impor- 
tance of ideas in the development of knowledge is 
that which is called by Whewell the "colligation of 
facts by means of an exact and appropriate concep- 
tion." Whewell states his view, and defends it 
against the objections of Mill, by calling attention 
to the presence of ideas in all our perceptions. He 
says, "All perception of external objects and occur- 
rences involves an active as well as passive process 
of mind ; — includes not only Sensations, but also 
Ideas by which Sensations are bound together, and 
have a unity given to them. From this it follows, 
that there is a difficulty in separating in our per- 
ceptions what we receive from without, and what 
we ourselves contribute from within." He, there- 



INDUCTION AND METHODS 379 

fore holds that, "we cannot obtain a sure basis 
of Facts, by rejecting all inferences and judgments 
of our own, for such inferences and judgments form 
an unavoidable element in all Facts. . . . We 
are not able, nor need we endeavour, to exclude 
Ideas from our Facts; but we may be able to dis- 
cern, with perfect distinctness, the Ideas which 
we include." In agreement with this position, 
what Whewell means by colligation is quite clear; 
it consists in bringing together a number of ob- 
served facts under a common description, as, to 
use one of his own illustrations, when Kepler, hav- 
ing made a number of observations on the suc- 
cessive positions of Mars, brought them together 
under the one conception of an ellipse. Mill con- 
tends that the method of colligation does not differ 
from an empirical generalisation, and since it 
involves no inference, it is not an induction. We 
do not need to go into the dispute between Whewell 
and Mill on these points ; it is clear, from the state- 
ments of what colligation means for Whewell, that 
ideas are essential to the existence of facts, and that 
a conception of the mind operates as a principle of 
connection between facts. The relation between 
fact and idea, however, is not always stated clearly 
by Whewell, for he sometimes speaks as if the in- 
ductive act consisted of a superinduction of concep- 
tions upon facts, that is, as if facts and ideas were 
external to each other. Green, in making the same 
point, says that "Whewell . . . spoils his own 
case (against Mill) by often writing as if the antith- 



380 A TEXT-BOOK OF LOGIC 

esis between ideas and facts were a valid one; as 
if the 'superinduction of ideas' upon facts were 
merely an operation that had to be performed ex 
parte nostra in order to give science." The value 
of Whewell's insistence upon colligation lies in this : 
it asserts that all our knowledge of the world of 
fact depends upon a more or less conscious exercise 
of the judging activity which carries us beyond a 
merely empirical generalisation, and enables us to 
regard the facts of observation under a new point 
of view. These points of view, our author contends, 
are supplied by, but are not necessarily derived 
from, the mind itself. As we shall see later, the 
point of view under which a group of facts becomes 
intelligible is sometimes ascertained by a stroke of 
genius, sometimes as the result of a laborious and 
diligent search. But however it may have been dis- 
covered, ideas and the facts that they make intelli- 
gible are not two discrete and mutually exclusive 
things; they are, as we have seen, only the reverse 
sides of a single experience. It is only by an act 
of analysis, as Whewell himself believes, that they 
can be distinguished. 

Parity of Reasoning. We often entertain beliefs 
about new facts on the ground of the similarity of 
these facts to other facts with which we are ac- 
quainted. For instance, if the bull dogs that we 
have known are unfriendly toward strangers, we 
shall shape our conduct toward any dog that has 
the general appearance of this breed in accordance 
with the belief that no bull dog likes strangers. 



INDUCTION AND METHODS 381 

This is an example of an empirical generalisation. 
From it may be distinguished another type of rea- 
soning which, while dealing with numbers of in- 
stances, affirms that we may entertain a belief about 
new facts, not because we have reason to entertain 
it about similar facts, but because we may apply 
to the new facts tests similar to those that were 
used on the old. That is, if we have shown that X 
is true of A, we may argue that it is true also of B, 
not because it is true of A, but for the same reason 
that it is true of A. This method of argument is 
called parity of reasoning. Mill's illustration is 
this: "Having shown that the three angles of the 
triangle ABC are together equal to two right angles, 
we conclude that this is true of every other triangle, 
not because it is true of ABC, but for the same rea- 
son which proved it to be true of ABC." Mill objects 
to calling this an induction on the ground that it 
"is not believed on the evidence of particular in- 
stances," that is, it is not proved in each of the in- 
stances, and, therefore, there exists no ground of 
inference from the known to the unknown cases. 
The importance of this type of reasoning at our 
present stage of inquiry is that it raises definitely 
the question whether numbers of instances are 
necessary for an inductive conclusion. 

REFERENCES. 

H. A. Aikins, The Principles of Logic, Ch. XXIV. 

B. Bosanquet, The Essentials of Logic, Lecture XI., a-d. 

J. E. Creighton, An Introductory Logic, 3d Edition, Ch. XIII. 



382 A TEXT-BOOK OF LOGIC 

J. G. Hibben, Logic, Deductive and Inductive, Part II., Chs. 
II., III., a,b. 

W. S. Jevons, Elementary Lessons in Logic, Lessons XXIV., 
XXV. 

S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
tion, Ch. VIII., §§ 1, 2. 

W. Minto, Logic, Inductive and Deductive, Book II., Chs. I, II. 

C. Read, Logic, Deductive and Inductive, 3d Edition, Ch. XV., 
§§ 1-4. 

ADVANCED 

B. Bosanquet, Logic, Vol. II., Book II., Chs. II., V, §§ 3, 4. 
F. H. Bradley, The Principles of Logic, Book II., Part II., 

Ch. II. 
W. R. B. Gibson, The Problem of Logic, Chs. XXXVII., 

XXXIX., XL., XLI. 
H. W. B. Joseph, An Introduction to Logic, Chs. XVIII. , 

XXIV. 
H. Lotze, Logic, Vol. II., Book II., Ch. VII. 
J. S. Mill, A System of Logic, Book III., Chs. I., II., III. 
F. C. S. Schiller, Formal Logic, Ch. XVIII. 
J. Venn, Empirical Logic, Ch. XIV., XXIV. 
J. Welton, A Manual of Logic, Vol. II., Book V., Chs. II., 

§ 146, III., § 148. 

QUESTIONS 

1. What do you assign to the distinction of truth and fact? 

2. In what two ways may the word fact be used, and what 
common element is present in both uses? 

3. 'Facts are objects that have been qualified by our 
thoughts about them.' Discuss. 

4. What is a category, and what is the relation of cate- 
gories to the judgment? 

5. What is a fact from the standpoint of the categories? 

6. What is meant by saying that reality is the world of 
fact? 



INDUCTION AND METHODS 383 



7. What light does the study of the worlds of fact throw 
upon the problem of monism and pluralism? 

8. How must we interpret the inductive problem, if by 
reality is meant the world of fact? 

9. What view of induction is implied in so-called perfect 
and imperfect induction? 

10. State and illustrate what is meant by perfect induction. 

11. State and illustrate what is meant by imperfect induc- 
tion. 

12. What is Mill's criticism of perfect induction? 

13. What is Bacon's estimate of imperfect induction? 

14. What is Bacon's estimate of perfect induction? 

15. What, according to Mill, is the value of imperfect in- 
duction? 

16. What is the value of perfect and imperfect induction as 
instances of simple enumeration? 

17. What is an empirical generalisation? 

18. Why, according to Mill, do we generalise our experience? 

19. 'Generalisation presupposes the existence of ideas.' Ex- 
plain. 

20. What is the value of empirical generalisation for 
science and for common life? 

21. State Whewell's conception and explanation of the col- 
ligation of facts. 

22. State Mill's objections to colligation. 

23. What is Green's criticism of Whewell's position? 

24. What is the essential truth of the doctrine of colliga- 
tion? 

25. What is parity of reasoning, and how does it differ 
from empirical generalisation? 

26. Why does Mill refuse to regard colligation as a truly 
inductive method? 

27. What is the importance of Mill's objection? 



384 A TEXT-BOOK OF LOGIC 



EXERCISES. 



1. Give at least six examples of what are known as facts, 
and distinguish the factual and truth elements in- 
volved in these examples. 

2. Make six statements of fact, and determine under what 
category each statement is made. 

3. Give three illustrations of what is known as reality as 
distinguished from fact. 

4. Give three illustrations each of perfect and imperfect 
induction. 

5. Write out two examples from common life and two 
from science of an empirical generalisation. 

6. Illustrate, by a carefully considered example, the mean- 
ing of a colligation of facts. 

7. Give three illustrations of parity of reasoning. 



CHAPTER XIV 

SOME DESCRIPTIVE METHODS OF INDUCTION 

Relation of Numbers of Instances to an Induction. 
The question with which we closed the last chapter, 
namely, whether numbers of instances are necessary 
for an induction, may be made the starting point 
of the present one. When induction is thought of 
as an inference based upon the examination of nu- 
merous instances of a phenomenon, it assumes, as 
we have seen, two forms : one, when we have assur- 
ance that all the instances are known; the other, 
when no such assurance can possibly be entertained. 
The former, we have considered, and it was said to 
be an illustration of a method of organising expe- 
rience that is not confined to any special kinds of 
fact, but is used over the whole extent of our life. 
The name that we gave to this method was empirical 
generalisation. The value of empirical generalisa- 
tions lies in the fact that they enable us to deal 
with large numbers of data in a simple way; we 
can deal with collections of fact as single facts 
whenever we ignore the differences and are inter- 
ested in the likenesses between the facts which enter 
into such collections. The assurance that every one 
feels in organising his experience in this manner is 
due to the limits within which it is consciously car- 
ried out. Empirical generalisations are held to 
apply only to the instances that have been examined. 

25 (385) 



386 A TEXT-BOOK OF LOGIC 

Numerous instances are necessary for an empirical 
generalisation, but such generalisations, since they 
do not carry us beyond the instances we have ex- 
amined, cannot be regarded as inductive inferences. 

The other form of induction by simple enumer- 
ation differs from the one just considered in the fact 
that not all the instances of the phenomenon have 
been observed, and the conclusion which the known 
instances are found to warrant is extended to other 
instances that have not come under observation. 
The question we are concerned with in such a case 
is whether, as Mill seems to hold, the validity of our 
inference is in proportion to the number of the in- 
stances examined, that is, whether the ground of the 
certainty of such an induction is found in the num- 
ber of the instances on which it is based ; or whether 
it is due to some other characteristic of the in- 
stances, for example, to the nature of the instances 
themselves. 

In attempting to answer this question, we may 
observe, in the first place, that the position held by 
Mill emphasises only one of the factors of an enu- 
merative induction, and that, even if we hold, with 
him, that it is an essential factor, it nevertheless 
depends for its effectiveness on the co-operation 
of another factor of which no special mention 
has as yet been made. For no one is prepared 
to maintain that the mere fact of numbers, irre- 
spective of the other qualities of the instances that 
an induction brings under review, can be the ground 
of an inference to other unknown instances. Mill's 



SOME DESCRIPTIVE METHODS OF INDUCTION 387 

position, therefore, must be understood to be that, 
although a greater degree of certainty attaches to 
any conclusion we reach respecting certain observed 
facts if the number of such observed facts is very 
great, and a lower degree of certainty if the number 
of such observed facts is relatively few, all the facts 
that enter into an induction must exhibit the qual- 
ities or relations with respect to which the induction 
is made; and that, if we extend to other instances 
the conclusion reached with respect to any one 
group of instances, this is possible because the new 
instances resemble the old ones in their essential 
nature. Whether, therefore, we are interested in 
arriving at an induction or in extending to new 
cases the conclusion of an induction already made, 
the fact of the common nature of all the instances 
must be established or assumed if the induction 
itself is sound, or if it is to make an inference pos- 
sible. In either case, the instances in question must 
all resemble one another in essential respects. 

We may remark, in the second place, that, in the 
light of what has now been shown, the question of 
the relation of numbers of instances to the validity 
of an induction is an interesting rather than the 
most important aspect of the inductive problem. 
There is no doubt, for example, that, within limits, 
our confidence in the conclusion of an induction is 
increased by the number of instances by which it is 
known to be supported. But we must distinguish 
between our confidence in a conclusion and the 



388 A TEXT-BOOK OF LOGIC 

ground on which the truth of that conclusion is 
supposed to rest; and, we must remember, it is 
with this latter question that we are here concerned. 
But we may say, even with respect to our confidence 
in the truth of inductive conclusions, that, beyond 
certain limits which vary for different phenomena, 
this is not affected in an appreciable manner by any 
considerable increase in the number of instances of 
a given phenomenon that may be brought to our 
attention. For example, should we not feel a jus- 
tifiable impatience with any one who, during the 
hours of only a single day, counted the number of 
objects within his observation that fell to the 
ground, and who informed us that that additional 
number of observed cases should be regarded as an 
additional reason for our confidence in the law of 
gravitation? And with respect to the truth of an 
inductive process, we may observe that the number 
of instances that need to be observed before a con- 
clusion is reached varies according to the nature of 
the instances themselves, and the ability of the par- 
ticular individuals who examine them. If this is 
true, the number of instances is a somewhat un- 
certain factor in the establishment of an induction, 
and there seems to be no reason why, if the nature 
and conditions of the observation are sufficiently 
unambiguous, the truth about a whole class of cases 
may not be reached as the result of the study of a 
single example. Indeed, in the history of science 
there have been instances in which some striking 
event has arrested attention, and set the problem 



SOME DESCRIPTIVE METHODS OF INDUCTION 389 

for the scientist, and in which the study of other 
examples of the same phenomenon has been under- 
taken mainly for the purpose of verifying the con- 
clusions reached with respect to the single instance. 
And, further, it may be said that, whether the truth 
of an induction has been reached as the result of 
an examination of one or many instances of a phe- 
nomenon, we may infer certain facts of other in- 
stances only when we assume that these also re- 
semble the old one or ones in essential respects. In- 
deed, this is only to state the significance that be- 
longs to all scientific statements whatever, and it 
gives the reason why all such statements are essen- 
tially hypothetical. Thus, if we suppose that P is 
a phenomenon under examination, and that X is 
the characteristic with respect to which it is finally 
determined, then we may say of any new example 
M that 'If M is P, it is X ;' that is to say, X is pred- 
icated of M, because it is P. We may, therefore con- 
clude, both with respect to the establishment of an 
induction and with respect to the possibility of ex- 
tending an induction to further instances of a phe- 
nomenon, that "the strength of an induction is not 
proportional to the number of instances cited. The 
generalisations that lead to the most trustworthy 
hypotheses are based, not on the counting of the 
number of instances, but on the weighing of their 
quality and character. One crucial instance may be 
worth a hundred others." 

Logical Significance of Statistical Methods. The 
progress of modern science has been associated so 



390 A TEXT-BOOK OF LOGIC 

intimately with the application of mathematical con- 
ceptions to concrete phenomena that the conclusion 
of the preceding paragraph may appear to be one- 
sided, if not erroneous. To meet this objection, we 
shall examine the logical character of the statistical 
methods, and ascertain their place in an inductive 
process. And, . at the outset, we should observe that 
whenever statistical methods are employed, the data 
under observation can most often be given only in 
the form of aggregates and averages. These meth- 
ods, as a rule, are applied distinctly for the purpose 
of ascertaining the numerical distribution of cer- 
tain characteristics which have come under obser- 
vation in a limited number of cases. Sometimes all 
that it is necessary or possible to do is to ascertain 
the total number of the recorded instances of the 
phenomenon. Usually, however, the interests we 
hope to satisfy by the use of the statistical methods 
are more specialised than this. For instance, we 
may wish to know what is the average occurrence 
of some irregular group character, as, for example, 
the average number of insane persons born per 
generation in a particular family. Or we may wish 
to ascertain the average amount of a constant group 
character, as, for example, the average amount of 
butter fat given per head by a particular breed of 
cattle. And even when these methods are applied 
to individuals, we still have in view the discovery 
of group characteristics. On this point Thorndike 
writes: "The sciences of human nature commonly 
use measures of individuals only in order to get 



SOME DESCRIPTIVE METHODS OF INDUCTION 391 

measures of groups. Not John Smith's spelling 
ability, but that of all fifth grade boys taught by a 
certain method; not A's delicacy of discrimination 
of weights, but that of all men; not B's wage, but 
that of all railroad engineers during a certain 
period ; not C's children, but the productivity of the 
English race as a whole ; not individuals, but groups, 
are commonly measured, compared and argued 
about." An examination of the individuals enu- 
merated in the census returns as to age, sex, married, 
unmarried, etc., also illustrates that interest in the 
characteristics of groups which prompts the use of 
distinctly statistical methods of inquiry. Sociological 
and insurance tables, as well as those of the phys- 
ical, biological and psychological sciences, are based 
upon the same interest. The particular service, 
therefore, that the employment of statistical meth- 
ods is able to render is to bind together diverse 
numbers of fact of a particular kind, and thus to 
provide a basis for the comparison of otherwise 
incomparable aggregates. "The method of count- 
ing . . . agreements and comparing results," 
says Gibson, "constitutes the Method of Statistics." 
The conclusions to which statistical inquiries 
lead are generalisations, but they are to be distin- 
guished from the empirical generalisations spoken 
of above in two respects. In the first place, statis- 
tical conclusions may be taken as a type of scientific 
as contrasted with empirical generalisation on the 
ground that they are the products of a systematic 
investigation of numbers of fact. By systematic in 



392 A TEXT-BOOK OF LOGIC 

this connection we mean that the basis of the class- 
ification of data is in each case consciously chosen, 
and that it is applied as a test of what can and what 
cannot be included in the numeration. For example, 
in an enumeration of houses in India, as Scripture 
points out, great difficulty was experienced on 
account of the indefiniteness of what was meant by 
a house. Similarly, the Weather Bureau would find 
it impossible to classify the hot, temperate, and cold 
days during a single year because of the indefinite- 
ness of the connotation of these terms. But if hot 
is defined as a shade temperature above 75°, cold 
as a shade temperature below 35°, and temperate 
any degree between these two, it is readily seen that 
there will be no difficulty in applying to the days 
of the year these tests, and generalising the results. 
In the second place, statistical conclusions are ex- 
pressed always in quantitative terms. This is, of 
course, not an accident; it is a result directly aimed 
at. In this way, certain features of the objects of 
our experience come to have a value and significance 
which, under any other method of observation, 
would be in danger of being overlooked altogether. 
For example, isolated events, and events that occur 
but rarely in our experience, unless they are very 
striking, are liable to receive but a passing notice, 
and to present but a small part of their meaning to 
such casual observation. It is also true that we are 
prone to overlook the import of those occurrences 
which are brought regularly to our notice. Famil- 
iarity breeds neglect as surely as do entire novelty 



SOME DESCRIPTIVE METHODS OF INDUCTION 393 

and strangeness. The average person seems to 
dwell in safety between these two extremes, with 
the result that the world presents him with few 
problems, and stimulates him but rarely to sus- 
tained intellectual effort. It is, however, a charac- 
teristic of the scientific mind that there is nothing 
so common that it does not deserve comprehension, 
and nothing so rare that it is beyond consideration. 
Out of this temper have been born those efforts to 
reduce the passing show of our daily experience to 
a definite system and order; and it has seemed, to 
those engaged in it, not the least worthy task, as it 
has been not the least profitable, to count the num- 
ber of times a given fact occurs, and to make num- 
ber a part of the facts themselves. Among the 
Greeks, Pythagoras interpreted the world in this 
mathematical way ; and all our modern sciences, the 
physical, biological and social, are employing statis- 
tics in the belief that when the relative frequency 
of the occurrences of a phenomenon is known, the 
phenomenon itself has been more accurately ob- 
served, and can be more exactly described. 

Qualitative Methods of Observation. Statistics, 
however, do not provide the only methods by which 
the observation of phenomena is carried on. There 
are classes of phenomena to which it cannot be 
fruitfully applied. We have said that whenever 
our material can be presented most advantageously 
in the form of aggregates and averages, statistics 
lend themselves as a means of bringing out features 
of this material that in no other way receives ade- 



394 A TEXT-BOOK OF LOGIC 

quate recognition. But we are not always or only 
interested in collective groups of objects. We are 
also interested in objects as instances of a genus, as 
instances in which the characteristics of a genus 
are given concrete expression. For instance, when- 
ever we call a certain flower a primrose, we are not 
describing the flower as an individual thing; rather 
are we neglecting altogether what is peculiar to the 
flower as an individual, what makes it this primrose 
rather than that ; and are recounting the character- 
istics which this object shares with an indefinite 
number of other specimens of the same species. The 
difference between this case and those that are 
amenable to statistical observation is that in the 
latter we need to collect together numbers of indi- 
viduals before the important characteristics are 
open to observation, whereas in the former, the indi- 
vidual instance displays all the attributes that are 
distinctive of the genus to which it belongs. Field 
botany, as our illustration suggests, is a descriptive 
science in the sense we are now indicating. Natural 
history and descriptive geology also belong to the 
same class. In these sciences, individual objects dis- 
play universal characteristics, that is, those which 
in our experience are found to belong to an indefi- 
nite number of other objects of the same kind or 
class. These common features of objects have their 
interest, and they set for us problems which tax our 
industry and challenge our efforts to solve. It is 
obvious, in the light of these statements, that the 
accurate knowledge which is the goal of our intel- 



SOME DESCRIPTIVE METHODS OF INDUCTION 395 

lectual life is not all of a single type, and that the 
methods of observation which we adopt or devise 
must be appropriate to the nature of the objects 
which are the material of our study. Sometimes 
we must avail ourselves of the quantitative methods 
of statistical observation, sometimes of the quali- 
tative methods of immediate perception. 

The Nature of Scientific Observation. Whatever 
the methods of observation may be, and however 
numerous, they are determined by the nature and 
purpose of observation itself. Now, in order to gain 
a clear understanding of the nature and purpose of 
observation, we may distinguish scientific observa- 
tion from the attitude we are accustomed to main- 
tain toward the ordinary events and circumstances 
of our every day life. Those adjustments with our 
environments which, during the course of our early 
years, we have succeeded in acquiring have been 
determined almost exclusively by practical consider- 
ations, and they have been maintained as the habits 
of our lives very largely on account of their value 
as instruments of physical and social survival. The 
earliest task that devolves upon the infant is to 
come into relations with the world around him, and 
his primary concern is with the world of material 
things from which he may receive either benefit or 
harm. It is only so far as it contributes to this end 
that, in its earliest beginning, the mind of the child 
is stimulated into activity, and his interest is 
aroused in the things and persons which constitute 
his world. Intelligence, that is to say, is a later 



396 A TEXT-BOOK OF LOGIC 

development than are those motor responses to 
environment through which the well-being of the 
individual is secured, and comes at first upon the 
scene of the individual's life, not in order to intro- 
duce any new interest or to initiate a new set of 
aims, but as the guide and servant of the practical 
which, through its means, is enlarged and rendered 
more efficient. These relations of the practical and 
intellectual in the order of their development throw 
an interesting light upon the function that intelli- 
gence plays in the maintenance of human existence ; 
for, as it was in the beginning, so does it remain for 
the greater part of each individual's life, there 
is no independent intellectual interest, and the func- 
tions of human understanding are determined 
throughout by the practical purpose which they 
instrumentally advance. If, in view of these con- 
siderations, we observe the characteristics of our 
ordinary life, we shall understand why, instead of 
displaying a careful attention to details, the per- 
ceptual consciousness has a conspective range which 
enables it to take in a large amount of detail with- 
out losing its practical effectiveness. What is not 
of practical importance fails to be noticed; only 
those features of the environment which are prac- 
tically important are gathered up and made objects 
of attention. 

How far perception, as it is ordinarily employed, 
is from giving accurate knowledge of the common- 
place facts and events of life is well known. As an 



SOME DESCRIPTIVE METHODS OF INDUCTION 397 

example of the unreliability of everyday observa- 
tion, we may cite the contradictory accounts of eye- 
witnesess of a common street accident. But, fur- 
ther, the conclusions and inferences that we base on 
such observations are, as a rule, no more trust- 
worthy than the observations themselves. In our 
daily life we exhibit constantly, what Whewell calls, 
" a vague and loose mode of looking at facts." As 
a result, to quote from the author just referred to, 
we remain "for a long time under the belief that a 
body, ten times as heavy as another, falls ten times 
as fast; that objects immersed in water are always 
magnified, without regard to the form of the sur- 
face; that the magnet exerts an irresistible force; 
that crystal is always found associated with ice; 
and the like. These and many others are examples 
of how blind and careless men can be, even in obser- 
vation of the plainest and commonest appearances ; 
and they show that the mere faculties of perception, 
although constantly exercised upon innumerable 
objects, may fail in leading to any exact knowl- 
edge." 

If now we consider what may properly be called 
scientific observation, we shall see that this differs 
from immediate perception in important respects. 
Scientific observation, in the first place, has not the 
conspective range of immediate perception, but is 
characterised by a close attention to detail within a 
limited field. This difference is conditioned by the 
difference in the purpose for which each exists. 
The purpose that controls the character and direc- 



398 A TEXT-BOOK OF LOGIC 

tion of our perceptions was seen to have its origin 
in the interests of our practical life. There is not, 
on the other hand, any such thing as observation in 
the strict meaning of the term, until our interest in 
the world of the practical life has failed to be satis- 
fied, either because the environment is too complex 
for perception to cope with, or because the relevant 
features of the environment have been hastily over- 
looked. In either case, importance comes to be at- 
tached to the details of a situation, and the condi- 
tions are favourable for the development of an in- 
terest in details quite apart from the regulation of 
our ordinary practical activities. Scientific obser- 
vation does not differ from immediate perception in 
the fact that the former is, and the latter is not, 
purposive, but in the character of the purpose which 
prescribes the goal and directs the course of each. 
In the case of scientific observation, the purpose 
that renders the details of an event or situation im- 
portant is theoretical; it springs from the interest 
we have in gaining an intimate acquaintance with 
these situations and events. That is to say, scien- 
tific observation must needs be used when we are 
launched upon a search for truth; it is an instru- 
ment of our acquisition of knowledge. What things 
are, and how they come to be what they are, are 
the questions which emphasise the necessity of accu- 
rate observation. 

In contrast with immediate perception, scientific 
observation is, in the second place, analytic ; it seeks 
in the environment for those features which are 



SOME DESCRIPTIVE METHODS OF INDUCTION 399 

relevant to the theoretical purpose by which it is 
guided. The difficulty that one experiences in his 
earliest scientific efforts is due to this selective 
character of observation. If, for example, we placed 
an histological preparation under the microscope, 
and, without any previous acquaintance with the 
subject to which it relates, we were to attempt to 
observe the character of the tissue, we should very 
likely fail; and our failure would be due probably 
to the fact that we had no defined purpose to guide 
our selection of the relevant detail. The beginner 
in any science is subjected to much loss of time and 
unnecessary discouragement if the instructor does 
not understand that scientific observation does not 
consist in looking at a mass of detail, but in looking 
for certain relevant aspects in a mass of detail. But 
to look for something relevant implies that a pur- 
pose is functioning in our examination of objects, 
and it is this purpose or idea which the capable 
instructor provides as the guide to his pupil's obser- 
vation. We observe only what we are prepared to 
observe, and mere collections of fact are useless 
until an idea illuminates and makes them intel- 
ligible. This view of scientific observation is illus- 
trated in the work of all the great scientists. It 
was conspicuously true, for example, of Darwin, 
of whom his son writes : "He often said that no one 
could be a good observer unless he was an active 
theoriser. This brings me back to what I said 
about his instinct for arresting exceptions, it was 
as though he were charged with theorising power 



400 A TEXT-BOOK OF LOGIC 

ready to flow into any channel on the slightest dis- 
turbance, so that no fact, however small, could avoid 
releasing a stream of theory, and thus the fact be- 
came magnified into importance." In other words, 
we observe not with our senses but with our intel- 
ligence. Or, as Huxley put it, what one sees when 
he looks through a microscope depends as much 
upon what is behind the eye-piece as upon what is 
under the objective. 

Experimental Observation. If we reduce the idea 
of a scientific experiment to its lowest terms, we 
may say that it consists in the interposition of an 
instrument of precision between our sense organs 
and the material we are studying. From this point 
of view, a scientific experiment secures an extension 
of the range of our perceptive organs, and, in so far 
as it does this, brings out more of the detail of the 
material under examination. The balances of the 
physicist, the microscope of the biologist, the tele- 
scope of the astronomer are devices for thus extend- 
ing the field of scientific observation. But there are 
limitations to experimental observation, as thus 
understood, which often would hinder the progress 
of truth if they were not offset by observation under 
normal conditions. Hence, as Lotze says, "Observa- 
tion often acquaints us with broad characteristics 
of phenomena, which in experiment would have 
been obscured by special conditions." The fact is 
that observation and experiment supplement each 
other, and there are cases when neither alone could 
lead us as far as when both are used in conjunction. 



SOME DESCRIPTIVE METHODS OF INDUCTION. 401 

There are also some phenomena to which experi- 
mental observation cannot be applied at all, and for 
our examination of these we must rely upon other 
means of observation. In this connection, it may be 
recalled that Darwin's great work was achieved by 
the method of observation, in the broad sense just 
described, rather than by the methods of experi- 
mental observation. 

A further consideration affecting our view of 
the range of scientific observation is that, however 
successful we may be in improving our present 
apparatus, and in devising and constructing new 
apparatus, there is, in all probability, a limit beyond 
which our sense organs are not capable of being 
supplemented in that way, and a point, consequently, 
at which the observations we make by the use of 
instruments of precision must stop. What the 
scientist does when he has reached his actual per- 
ceptual limits, and what he would attempt to do if 
he reached the theoretically possible limits of per- 
ception, is to supplement his actual observations 
by guesses as to what, if perception were possible, 
further observation would, in all probability, make 
known. In some such way as this have the lumin- 
iferous ether, atoms, ions, etc., become parts of the 
actual working data of science, data, be it remarked, 
that are regarded, by science, as truly material sub- 
stances as are the grosser bodies that are now within 
the range of present perception. This kind of obser- 

26 



402 A TEXT-BOOK OF LOGIC 

vation we may call, for the sake of convenience of 
reference, theorising, or theoretical observation. 

Another characteristic of experimental observa- 
tion is that, like all observation, it must be used in 
the service of the purpose which directs the obser- 
vation. Hence the impossibility of any one being 
an experimental scientist who is not thoroughly 
acquainted with the mechanical structure of the 
apparatus which he either uses or designs. There 
is a quite prevalent notion, especially among stu- 
dents and inexperienced instructors, that one is 
necessarily an experimentalist if he works in a 
laboratory and manipulates apparatus. To these, 
no question could come with more pertinence than 
this: 'For what purpose are you using this par- 
ticular piece of apparatus, and precisely in what 
way does it enable you to realise this purpose?' It 
is not apparatus that lends significance to our ideas, 
but ideas that make our apparatus intelligible in- 
struments of observation. To lose sight of this 
truth is to miss entirely the true meaning of experi- 
mental science ; for we may be as passively assimil- 
ative when looking through a microscope as we 
might be actively observant when using our natural 
organs of perception. But when our apparatus 
"passes into the service of an idea, and we proceed 
to put our object under such conditions as the idea 
requires for testing and verifying itself, our obser- 
vation is no longer merely passive, but experi- 
mental. A definite, purposive interference of some 
sort with the production of the phenomenon to be 



SOME DESCRIPTIVE METHODS OF INDUCTION 403 

noted is the desideratum" of experimental observa- 
tion. 

At precisely what point can this interference 
with the phenomenon be introduced most advanta- 
geously? The answer to this question is given 
unanimously by all the workers in the field of 
science. Science seeks to control, not the nature, 
but the conditions of the occurrence of phenomena. 
"To observe with accuracy and convenience," says 
Jevons, "we must have agents under control, so as 
to raise or lower their intensity, to stop or set them 
in action at will." Welton writes: "Appeal to ex- 
periment is, then, necessary whenever simple obser- 
vation alone will not make plain all the essentials 
of a phenomenon; and its object is to eliminate all 
the conditions which are not specially operative in 
the particular case under observation." In like 
strain Gibson says: "Control over the conditions 
under which the object shall present itself for study 
is the great desideratum and the factor in experi- 
mental observation which most influences the pre- 
cision and certainty of the results obtained. Such 
control enables us to vary the circumstances, and to 
repeat the observation as often as we please by 
simply reproducing the concurrence of conditions 
requisite for bringing into play the desired effect." 

REFERENCES 

SEE THE END OF THE NEXT CHAPTER 



404 A TEXT-BOOK OF LOGIC 



QUESTIONS 

1. What are nature, extent and value of empirical general- 
isations? 

2. Does an empirical generalisation involve an inductive 
inference? What is your reason? 

3. Are numerous instances of a phenomenon necessary for 
an empirical generalisation? Why? 

4. Can imperfect induction be regarded as an example of 
an inductive inference? State reasons for your answer. 

5. What problem is involved in the fact that the con- 
clusions of imperfect induction are extended to unex- 
amined instances of the phenomenon in question? 

6. What is Mill's position on the validity of imperfect in- 
duction? 

7. What influence does the fact that a large number of in- 
stances of a phenomenon have been examined have on 
the validity of an inductive inference? 

8. What value may we give to number of instances in an 
inductive process? 

9. What fact with respect to the nature of induction is in- 
volved in the hypothetical character of scientific state- 
ments? 

10. What particular interest determines the use of statis- 
tical methods? 

11. State and illustrate some of the questions that statis- 
tical methods enable us to answer? 

12. What purpose does the application of statistical methods 
to individuals commonly serve? 

13. In what respects do statistical conclusions differ from 
empirical generalisations? 

14. Describe the particular method of observation employed 
by field botany, natural history and descriptive geology. 

15. What are the characteristics of perception, and in what 
relation does perception stand to intelligence? 



SOME DESCRIPTIVE METHODS OF INDUCTION 405 

16. In the light of your answer to the previous question, 
what view must be taken of the logical function of per- 
ception? 

17. In what respects does scientific observation differ from 
ordinary perception? 

18. What do you understand by experimental observation? 

19. What are the limits of experimental observation? 

20. Explain the nature of theoretical observation. 

21. Illustrate by reference to the relation of the scientist to 
his apparatus the place of purpose in experimental ob- 
servation. 

22. 'Experimental observation involves a purposive inter- 
ference with the production of phenomena.' Explain. 

23. State what a scientist may and may not do in inter- 
fering with the phenomenon he wishes to observe. 

EXERCISES 

1. Give at least six examples of empirical generalisation. 

2. Give six illustrations of imperfect induction, and show 
how each may be used as the basis of an inference. 

3. Illustrate from each of the sciences you have studied 
the hypothetical character of inductive inference. 

4. Show, by a carefully worked out example, the nature 
and method of statistical observation. 

5. Give one example of experimental observation. 

6. Illustrate what is meant by theoretical observation. 



CHAPTER XV 

SOME EXPLANATORY METHODS OF INDUCTION 

The Nature of Scientific Explanation. The meth- 
ods that were examined in the last chapter may be 
classified roughly as methods of observation, and 
those that are to be examined in the present chapter 
may be classified approximately as methods of ex- 
planation. It will, perhaps, help us to understand 
these latter methods if in this section we inquire into 
the meaning of the term explanation. This is the 
more necessary because some confusion on this sub- 
ject has been occasioned by the way in which scien- 
tists have sometimes expressed themselves with 
respect to the aims of science. For example, one 
declares that science consists of a complete descrip- 
tion of the phenomena that are brought under 
observation, while another declares as emphatically 
that description is only a preliminary step in the 
work of the scientist, and that the goal of all science 
is explanation. If we were to take such statements 
absolutely, we should be led to suppose that there 
is between the scientists an irreconcilable differ- 
ence of opinion as to the nature of the work in 
which they are engaged, and we might presume 
that, until they arrived at a settlement of these 
differences, it were useless for us to discuss the 
matter further. This, however, would be a false 
view to take; for not only must logic examine the 

(406) 



SOME EXPLANATORY METHODS OF INDUCTION 407 

aims and methods of the sciences, but the differ- 
ences already referred to are verbal rather than 
real, and are due in a large measure to the ways in 
which what is after all a substantial agreement has 
happened to get itself expressed. 

Let us first get before ourselves what is meant 
ordinarily by a scientific explanation, and then, in 
the light of this information, we may consider the 
distinction between it and scientific observation. 
All scientific explanation conforms to a very simple 
type; it consists in stating what other things occur 
when the particular thing we are observing occurs. 
If, for example, I hold a book in my hand and, re- 
leasing my grasp upon it, it falls to the ground, we 
should ordinarily explain the falling of the book to 
the ground by saying that I had released my hold 
upon it. The book fell because I released my hold. 
If, now, experimenting with other objects than 
books, I find that pencils, stones, silverware, china- 
ware, etc., fall to the ground when the hand that 
held them releases its grasp, I may put the results 
of these observations into the statement that 'all 
objects fall to the ground when their support is re- 
moved.' If, further, the fall not only of the book 
but of all objects whatsoever is connected with the 
force of gravity, the process of explanation has been 
carried a step farther. But however far such a 
process is carried, it consists essentially in describ- 
ing events that occur along with the event which, at 
the beginning, was the object of our observation. 
'This occurs when that occurs' is the universal for- 



408 A TEXT-BOOK OF LOGIC 

mula which reveals the nature of scientific explan- 
ation. 

The same view is sometimes expressed more pre- 
cisely in the statement that scientific explanation 
is concerned with the discovery of the conditions of 
the occurrence of any object of observation. Let 
P be the phenomenon or object observed, then the 
question of explanation relates to the conditions, C, 
under which it occurs. When these conditions have 
been discovered and recorded, we are said to have 
explained the phenomenon. Out of the innumerable 
circumstances that accompany an event, the prob- 
lem of scientific explanation is to select those which 
must be present whenever the event is present, and 
which when they are absent the event itself does not 
occur. The factors of explanation are always 
found among the concomitant circumstances of the 
phenomenon which comes before us for explanation. 
An examination and description of these is what is 
meant by a scientific explanation. 

With these statements in mind, we may now 
make clearer the distinction between scientific ob- 
servation and explanation. It is obvious, in the 
first place, that the phenomena which we include 
under each of these terms are continuous with each 
other. For instance, the falling of an object is con- 
tinuous with the release of the hand's grasp upon it. 
Stated generally, a phenomenon and its conditions 
form an inter-connected series of events, no one of 
which is unnecessary to the series, and each of which 
is important if the series is to maintain its essential 



SOME EXPLANATORY METHODS OF INDUCTION 409 

character. From this point of view, the distinction 
between a phenomenon and its conditions is more 
or less accidental and artificial ; and if we take such 
series as scientific units, regarding the objects 
which are the starting points of our observations 
as fragments which through scientific methods we 
are to supplement by their necessary concomitants, 
we shall see that the whole aim of science has been 
fulfilled when such a series has received a full and 
complete description. If, in the second place, we 
do not regard the object which provides us with 
the starting point of our observation as a fragment, 
but as a phenomenon which has a quasi-independent 
existence, we shall be inclined to consider the search 
for conditions as a distinct step in scientific investi- 
gation, and, laying emphasis upon this, the problem 
of explanation will assume larger proportions than 
it did in the other view. But whichever of these 
two ways of looking at the scientific problem we 
may take, the factors of each are the same, and be- 
tween these views there is only a verbal difference. 
On either view, we have to supplement what is 
given — the phenomenon, with what is not given — 
the conditions; and to determine the conditions of 
a phenomenon is what we understand as the prob- 
lem of scientific explanation. 

The Meaning of Analogy. The word analogy is 
used in different senses, and these we shall proceed 
to distinguish. It is used, in the first place, to indi- 
cate an identity of relation. This is the meaning 
that it had for Aristotle with whom it corresponded 



410 A TEXT-BOOK OF LOGIC 

to mathematical proportion. In this sense, it as- 
sumes the form of 2 : 4 : : 3 : 6, where the relation 
between 2 : 4 is identical with the relation between 
3 : 6, and the factors between which the relation 
obtains are homogenous. We may state the charac- 
teristics of this first meaning of analogy generally 
by saying that whenever a is related to b in the same 
way that c is related to d, then whatever follows 
from a : b follows also from c : d, if the inference 
is based upon nothing but the identity of the rela- 
tion between the two pairs of factors or terms. 

The word analogy is used, in the second place, 
to indicate a similarity of relation. The difference 
between this and the preceding use of the term is 
not due to the absence of proportion, but to the dif- 
ference in the character of the terms between which 
the proportion obtains. Although the relation be- 
tween two pairs of terms is similar, the terms be- 
tween which the relation holds may be heterogene- 
ous. For example, the number of vibrations per sec- 
ond of the sound which is recognised by our musical 
sense as middle C (c') is 261, that of its octave (c") 
is 522 (2x261). The similarity of relations in- 
volved in these facts is expressed in the proportion 
261 : 522 : : c' : c". But since the octave of any 
musical note always has twice as many vibrations 
as the note itself, we may express the law of octaves 
in the proportion : x vibrations of air : 2 x vibra- 
tions of air : : a note : its octave. The analogy may 
be interpreted to mean that the relation between 
the series of physical stimuli is connected in our 



SOME EXPLANATORY METHODS OF INDUCTION 411 

knowledge with their corresponding impressions 
in such a way that given the former we can infer 
the latter. 

The word analogy is used, in the third place, to 
indicate any resemblance between things. Here the 
idea of proportion which was present in the preced- 
ing uses has dropped out, and resemblance of any 
kind between objects is made the basis of analogical 
inference. For example, certain resemblances were 
early known to exist between sound light : that both 
were capable of being reflected, that the direction 
of reflection of each obeyed the same law, that the 
angle of reflection is equal, in each case, to the angle 
of incidence. It was further known that sound 
travelled in waves. From these data it was inferred 
analogically that light also travelled in waves. If 
it had been known that the equality of the angles 
of reflection and incidence in the case of sound were 
due to its traveling in waves, the inference to a like 
mode of propagation in the case of light would have 
been more certain. The more important the re- 
semblances, that is to say, the more certain the in- 
ference. From the example just used, the analogy 
between things may be expressed generally in the 
following manner: If a resembles b in certain re- 
spects, x, and a exhibits the character y, it is in- 
ferred that b will resemble a in possessing the char- 
acter y also. 

The Logical Character of Analogy. We have 
shown that analogy is a method of inferring cer- 
tain possible events on the ground of a resemblance 



412 A TEXT-BOOK OF LOGIC 

between certain ascertained events. "In the syllo- 
gism of Analogy," says Hegel, "we conclude from 
the fact that some things of a certain kind possess 
a certain quality, that the same quality is possessed 
by other things of the same kind." In every argu- 
ment from analogy an identity of some sort is as- 
sumed, and it is upon the character of the assumed 
identity that the validity of the inference is in every 
case said to depend. Let us look at the soundness 
of such arguments in the light of this statement. 

In the first place, it is obvious that not any kind 
or degree of resemblance is a safe principle of in- 
ference. In common life, we meet with analogical 
arguments that are very superficial. For instance, 
the loyalty of college students to the university from 
which they were graduated may often lead to a 
mistaken estimate of a man who is a graduate of 
the same university. "It would be a very bad anal- 
ogy," as Hegel remarks, "to argue that since the 
man Caius is a scholar, and Titus also is a man, 
Titus will probably be a scholar too; and it would 
be bad because a man's learning is not an uncondi- 
tional consequence of his manhood." In public ad- 
dresses on political and social questions we may 
often detect arguments of this sort. In the period 
of the Commonwealth in England, the demand for 
annual Parliaments is said to have been urged on 
the ground that the serpent — which is the wisest 
of beasts — sheds his skin every year. We also find 
analogical reasoning in the works of men of science, 
and sometimes the conclusion which these argu- 






SOME EXPLANATORY METHODS OF INDUCTION 413 

ments are intended to support rest upon a very 
weak and even false resemblance. Take, for in- 
stance, the conception of the human body ts a 
machine. "When we desire to set machinery in 
operation," as Chittenden, commenting on this view, 
says, "we must get up steam, and so a fire is started 
under the boiler and steam is generated in propor- 
tion as fuel is burned. The source of the energy 
made use of in moving the machinery is the extra- 
neous combustible material introduced into the fire- 
box, but the energy of muscular contraction, for 
example, comes not from the oxidizable food mate- 
rial in the stomach, but from the material of the 
muscle itself. In other words, in the animal body it 
is part of the tissue framework, or material that is 
closely incorporated with the framework, that is 
burned up, and the ability to endure continued mus- 
cular strain depends upon the nutritive condition of 
the muscles involved, and not upon the amount of 
food contained in, or introduced into, the stomach." 
In the second place, the resemblances upon which 
analogical arguments are made to rest must be im- 
portant resemblances. Accidental resemblances and 
superficial likenesses are at the basis of all falla- 
cious reasoning by analogy. With this class of anal- 
ogies in mind Heine was led to exclaim, "Heaven 
defend us from the Evil One and from metaphors." 
But if the resemblance is essential and important, 
there is no need to avoid the use of this method of 
reasoning. Now when we speak of a resemblance 
being essential, we mean that the characteristics 



414 A TEXT-BOOK OF LOGIC 

with respect to which objects are compared must be 
essential either to the existence of the objects or to 
the purpose which these objects realise. If, to illus- 
trate the former case, we infer that certain things 
are true of diamonds because they are true of 
graphite, we, no doubt, do so with the thought in 
mind that these substances are different forms of 
carbon. To illustrate the latter, we may argue from 
the similarity in shape of certain flints found in the 
ground and those used by certain savage tribes of 
the present day that the former were used as 
weapons since this is the use that the latter are 
known to have. 

In the third place, analogical arguments must 
take into account not only the importance of the 
resemblances but the non-importance of the differ- 
ences between the objects compared. An interest- 
ing example is the following, borrowed from Gib- 
son. He says, "we might enumerate many points 
of external resemblance between the Whale and the 
Shark, and found upon them an analogical argu- 
ment to the effect that the respiration-processes in 
the two animals must be similar. The whale, we 
might say, resembles the shark not only in all the 
common characters of Vertebrates, but also in its 
submarine habitat and in being (as regard species) 
one of the very largest of marine animals. Like the 
shark, it is fish-like in external form, its fusiform 
body being well fitted for cleaving the water. An- 
teriorly its body passes into the head without any 
distinct neck, and posteriorly it is furnished with a 



SOME EXPLANATORY METHODS OF INDUCTION 415 

swimming-tail into which the body gradually tapers. 
It has no hairy covering. Like the shark, again, 
it has a wide mouth, and it is of predaceous habit, 
feeding only on living animal nutriment. There- 
fore we may with great probability conclude that 
its method of respiration is like that of the shark — 
i. e., that it breathes the oxygen dissolved in the 
water, and has no need to be supplied with atmos- 
pheric air. 

"But this argument would be unsound. The points 
that we ought to have observed are the characters 
connected ivith the function of respiration. The 
presence of gill-slits in the shark and their absence 
in the whale is a difference so essential to the in- 
quiry that its observation would at once have been 
sufficient to make our analogy fall to the ground. 
And among the still more obvious external differ- 
ences there is a single character which also should 
alone outweigh all the above mentioned resem- 
blances. The extremity of the shark's tail is ex- 
panded vertically ; in the whale the flukes of the tail 
are placed horizontally. From many points of view 
this difference might be regarded as unimportant; 
but from the point of view of our analogical argu- 
ment it is very important indeed, for it is intimately 
connected with the problematic point of resemblance 
that we are endeavouring to establish. For sea- 
creatures which, like the whale and the shark, spend 
their life in swimming freely through the water, 
the direction of movement is chiefly determined by 
the presence or absence of the air-breathing habit. 



416 A TEXT-BOOK OF LOGIC 

Those creatures that have no need of atmospheric 
air move usually in straight-forward and lateral 
directions, and for effecting such movements a ver- 
tically expanded caudal fin is admirably fitted. But 
creatures that need to rise frequently to the surface 
of the water for the purpose of respiration are con- 
stantly moving upward and downward. To move- 
ments of this kind a tail with horizontally expanded 
fluxes is precisely adapted. Thus the whale's hori- 
zontally expanded tail affords a strong presumption 
in favour of the presence of the air-breathing habit ; 
and this apparently trifling difference between the 
two creatures must be regarded as fatal to the 
cogency of the analogical argument." 

The Function of Analogy in Induction. We have 
been considering analogy as a special kind of argu- 
ment, the way in which Aristotle understood it. We 
proceed now to discuss the value that analogies have 
for advancing our knowledge of the world about us, 
the assistance they may give in the problem of ex- 
planation. Analogy, as our exposition has shown, 
is an argument from similar instances. It is, to 
quote Mellone, "any resemblance between things 
which enables us to believe of one what we know 
of the other." We advance from one instance to 
another on the basis of a perceived or imagined sim- 
ilarity between the instances. The necessity of ad- 
vancing in an analogical argument from particular 
to particular, has led to the saying that analogy 
"sticks in the particular instances." Although this 
is true, it is not on that account worthless as an in- 



SOME EXPLANATORY METHODS OF INDUCTION 417 

strument or means of arriving at the law of the 
connection between resembling instances. For if 
there is a resemblance, or a group of resemblances, 
between P and P', such that we feel warranted in 
affirming of P' what we know positively only of P, 
we may look upon the similarity, not merely as a 
bridge from the one instance (P) to the other (P'), 
but as a suggestion of a specific connection between 
the two instances which is not brought out ex- 
plicitly by the analogy. It is this characteristic of 
suggesting more than it can possibly make clear, 
that renders analogy of service in an inductive proc- 
ess. The following remarks are intended to make 
this point clear. 

Two things are characteristic of analogy. In the 
first place, the comparison of instances, as we have 
seen, rests upon what are called their essential 
attributes, but, in the second, the degree of the 
resemblance always remains more or less undeter- 
mined. When we have assured ourselves that the 
resemblance depends upon essential features of the 
compared phenomena, we are, however, still in 
doubt about the precise factor or factors in the re- 
semblance upon which the inferred characteristic 
really depends. Thus any two phenomena, P and 
P', may resemble each other in possessing the 
attribute x, a resemblance which seems to warrant 
us in expecting that if P also shows the character- 
istic y, P' will likewise show the same characteristic. 
To take a concrete example. The chemist classifies 

27 



418 A TEXT-BOOK OF LOGIC 

a number of elements together under the head of 
alkaline metals because all these elements — potas- 
sium, sodium, caesium, rubidium, and lithium, — 
possess certain characteristics in common; for in- 
stance, their active combination with oxygen to de- 
compose water at all temperatures; their forming 
strongly basic oxides, highly soluble in water, yield- 
ing powerful caustic and alkaline hydrates from 
which water can not be expelled by heat; the solu- 
bility of their carbonates in water; and the forma- 
tion by each metal of only one chloride. Now, if in 
the progress of the chemistry of any one of these 
metals a new property is discovered, it is natural 
to infer by analogy that the other members of the 
group will display under appropriate conditions the 
same property. But beyond the suggestion of a 
connection of the new property with the character- 
istics of the alkaline group analogy cannot go; it 
cannot point out on which attribute, or combination 
of essential attributes, the new property really de- 
pends. Thus an argument by analogy presumes a 
connection between x and y, but it cannot show that 
y depends on x rather than on some other property 
in P which may not belong to what we have called 
its essential attributes. However strong the pre- 
sumption may be that x and y are causally related, 
there always remains the possibility that y is condi- 
tioned in some other way. Analogical arguments 
for this reason are never conclusive, and in an in- 
ductive process they are valuable only because they 
suggest lines of further observation which may 



SOME EXPLANATORY METHODS OF INDUCTION 419 

either verify or discredit the analogical inference. 
Mill, therefore, is right when he regards an analogy 
as "a mere guide post, pointing out the direction 
in which more vigorous investigations should be 
prosecuted. It is in this last respect," says Mill, 
"that considerations of analogy have the highest 
scientific value. The cases in which analogical evi- 
dence affords in itself any very high degree of prob- 
ability are, as we have observed, only those in 
which the resemblance is very close and extensive; 
but there is no analogy, however faint, which may 
not be of the utmost value in suggesting experi- 
ments or observations that may lead to more posi- 
tive conclusions." With this view, to which Mill 
does not consistently adhere, Jevons is in agree- 
ment, and he has made it the foundation of his chap- 
ter on analogy in the Principles of Science. 

Nature of Hypothesis. An hypothesis is an at- 
tempted explanation of an occurrence, a supposition 
about the connection of particular phenomena. To 
get the meaning of this general statement before us, 
let us consider a particular case. Malaria is a dis- 
ease which has a set of characteristic symptoms, 
the chief of which are chills and fever occurring at 
more or less definite intervals of time. When the 
physician has become familiar with the character- 
istic symptom complex of the disease, he is able to 
diagnose the new cases that come under his obser- 
vation by means of the similarity that they bear to 
this complex ; all the cases that show the diagnostic 
marks of the disease he calls malaria. The logical 



420 A TEXT-BOOK OF LOGIC 

procedure in this instance is analogical. If, how- 
ever, instead of taking the physician's attitude which 
requires him to diagnose only for the purpose of 
selecting the proper remedies, we approach the dis- 
ease from the standpoint of the scientist who wants 
to know what malaria is, we shall have to go beyond 
the similarities which figure in the physician's diag- 
nosis, and, by a series of suppositions or hypotheses, 
work our way among the antecedents and concomi- 
tants of the cases of the disease for some clue to the 
agent which is responsible for the production of the 
disease. It is not enough to say that similar symp- 
toms mean the same disease,, the question we are now 
asking is what produces the similar symptoms in all 
the cases that occur. We are looking for something 
more than similarity, we are searching for an iden- 
tity among the conditions under which the disease 
is contracted. Thus, for example, night air, damp 
places, exhalations from marshy ground have been 
proposed as the antecedent condition which is 
capable of producing malarial fever. It is only 
within comparatively recent times that, for these 
hypotheses, another has been substituted which con- 
nects the disease with the bite of the Anopheles 
mosquito, and this is the view that is held at the 
present day. The bite of the Anopheles mosquito* 
is our hypothesis for the occurrence of malaria. 

In the light of this illustration, we may observe 
that not any supposition about phenomena is an 
hypothesis. It is only when the supposition points 
us to phenomena of the same order as the event 



SOME EXPLANATORY METHODS OF INDUCTION 421 

that we are trying to explain that it satisfies the 
conditions of a tenable hypothesis. In medicine, 
for example, we no longer entertain theological ex- 
planations of disease, and for devils we are substi- 
tuting bacteria and their toxins, and in those dis- 
eases which cannot be shown to be of bacterial 
origin, as for example many of the occupational 
diseases, we assign either a chemical cause, as in 
lead poisoning, or a mechanical one, as in the dis- 
ease characteristic of the Sheffield steel grinders. 
When made with regard to the requirement we are 
now considering, namely, that the supposition 
should be stated in terms of the same order as the 
phenomenon to be explained, hypotheses differ from 
one another only in the degree of their probability; 
and it seems to us to be quite misleading to speak of 
them as guesses, as is done by some logicians, as if 
they were altogether uncontrolled by the nature of 
the phenomena for which an explanation is being 
sought. The truth of this statement is apparent 
when we recognise that the demand for an hypoth- 
esis is only a particular form of the demand for a 
careful analysis of the phenomena under observa- 
tion. Our acquaintance with objects becomes more 
minute as well as more accurate under the stimulus 
that comes from the call for explanation ; and if one 
step in the process of explanation is hypothetical, 
that step must still be controlled by the nature of 
the observed material if we are to safeguard the in- 
ductive process against useless and irresponsible 
guesses. The satisfaction of this requirement by 



422 A TEXT-BOOK OF LOGIC 

science may be briefly illustrated. To account for 
the phenomena of sound, the physicist, starting with 
the sound experience, connects this with the undu- 
lations of the air which occasion it, and these undu- 
lations, again, he connects with a vibrating body, — 
a stretched string, the vocal cords, an organ pipe. 
When the scientist asks what is the source of the 
phenomena of light which occasion the sensation of 
vision, although he cannot point definitely to the 
material bodies which produce the undulations in 
the ether, he forms his hypothesis in terms of the 
same order as the phenomena that he has under in- 
vestigation; and he does so because the "scientific 
imagination," to quote Tyndall, "demands, as the 
origin and cause of a series of ether-waves, a par- 
ticular vibrating matter quite as definite, though it 
may be excessively minute, as that which gives 
origin to a musical sound. Such a particle we name 
an atom or a molecule. I think the intellect, when 
focussed so as to give definition without penumbral 
haze, is sure to realize this image at last." 

Objections to the Use of Hypothesis. Although 
the history of modern science furnishes so many 
illustrations of the value of hypotheses, and al- 
though the methods in use at the present day for 
the advancement of scientific knowledge depend 
also upon their employment, there is, nevertheless, 
among scientific men either only a half-hearted 
recognition of their services, or a misleading rejec- 
tion of their claims to a place in scientific procedure. 
This interesting fact is not difficult to understand, 



SOME EXPLANATORY METHODS OF INDUCTION 423 

and we refer to it here because it enables us to 
explain some aspects of the formation of hypoth- 
eses which as yet have not been mentioned. The 
hesitancy of men of science to recognise that the 
advancement of scientific knowledge is, in any re- 
spect, dependent upon hypotheses, may be attrib- 
uted to their effort to exclude from all parts of their 
work influences and additions that are derived from 
the nature of the mental processes through which 
that work is carried on. The aim of science is 
throughout objective in the sense that its task is to 
describe and explain the facts of observation, to 
arrive at judgments about these facts that are inde- 
pendent of the idiosyncrasies of the individual mind. 
"The scientific man," as Karl Pearson says, "has 
above all things to strive at self-elimination in his 
judgments, to provide an argument which is as true 
for each individual mind as for his own." The 
life of science depends upon loyalty to this aim. 
The intellectual integrity of every scientific man is 
involved in his efforts to maintain this aim. All 
this may be granted; it may even be admired and 
praised. And yet we cannot avoid the impression 
that if the spirit of loyalty to professional ideals 
which is displayed by workers in the fields of the 
particular sciences were supplemented by an ac- 
quaintance with the history of scientific achieve- 
ments, the objections to hypothesis would be miti- 
gated, and in time might entirely disappear. For 
the admission of hypothesis in no way interferes 
with keeping the work of science objective, and 



424 A TEXT-BOOK OF LOGIC 

their practical rejection may often render impos- 
sible of realisation the aims which stimulate scien- 
tific effort. 

The situation that has just been described may 
be made more explicit by saying that without an 
active and fertile imagination, it is impossible to 
formulate a satisfactory hypothesis. It is, in part, 
because the scientist does not take the pains to 
ascertain what are the nature, conditions, and limits 
of the imagination that he looks askance upon the 
formation of hypotheses. This is not the place to 
state and develop a doctrine of the imagination; it 
is enough for our purpose to call attention to the 
fact that many of the leading men of science have 
borne eloquent testimony to the value of the imagi- 
nation in advancing the interests of scientific truth. 
In his address on 'Scientific Use of the Imagination/ 
Tyndall writes: "Bounded and conditioned by co- 
operant reason, imagination becomes the mightiest 
instrument of the physical discoverer. Newton's 
passage from a falling apple to a falling moon was, 
at the outset, a leap of the imagination." Tyndall 
prefixed to his essay the following passage from an 
address to the Royal Society by Sir Benjamin Brodie. 
"Lastly, physical investigation, more than anything 
besides, helps to teach us the actual value and right 
use of the Imagination — of that wonderful faculty 
which, left to ramble uncontrolled leads us astray 
into a wilderness of perplexities and errors, a land of 
mists and shadows; but which, properly controlled 



SOME EXPLANATORY METHODS OF INDUCTION 425 

by experience and reflection, becomes the noblest 
attribute of man; the source of poetic genius, the 
instrument of discovery in Science, without the aid 
of which Newton would never have invented flux- 
ions, nor Davy have decomposed the earths and 
alkalies, nor would Columbus have found another 
continent." In his Methods and Results, Huxley 
writes : "It is a favourite popular delusion that the 
scientific inquirer is under a sort of moral obliga- 
tion to abstain from going beyond that generalisa- 
tion of observed facts which is absurdly called 
'Baconian' induction. But any one who is practically 
acquainted with scientific work is aware that those 
who refuse to go beyond fact rarely gets as far as 
fact; and any one who has studied the history of 
science knows that almost every great step therein 
has been made by 'anticipation of nature/ that is, 
by the invention of hypotheses which, though veri- 
fiable, often had little foundation to start with, and 
not infrequently, in spite of a long career of useful- 
ness, turned out to be wholly erroneous in the long 
run." 

These quotations are sufficient to illustrate the 
importance of the imagination in the construction 
of scientific hypotheses, and to indicate the reason 
why many men of science look with suspicion upon 
the use of hypotheses. "Scientific men fight shy of 
the word (imagination) because of its ultra-scien- 
tific connotations," because its use is often uncon- 
trolled, and because under the best conditions it 
sometimes leads us astray. But to reject an instru- 



426 A TEXT-BOOK OF LOGIC 

ment of research because of its limitations is no 
more reasonable than would be a physician's refusal 
to employ strychnine in the cure of a patient, be- 
cause that drug is on the commercial market in the 
form of 'Rough on Rats/ We are not advocating an 
indiscriminate exercise of the imagination, nor the 
substitution of it for the careful and painstaking 
observation of phenomena. What we are pointing 
out is that there are conditions of physical investi- 
gation which render all known instruments of pre- 
cision inadequate and clumsy tools, and that if 
observation is not to be hindered its range must be 
extended as far beyond that of our instrumental 
world as this is beyond the world made known by 
our natural organs of perception. We cannot, for 
example, bring under observation by the most 
powerful microscope the particles of matter which 
are the media in our atmosphere of reflected light. 
By what means has the existence of such particles 
scattered throughout our space come to be believed 
in? Tyndall cites this example as an illustration 
of the use that science may make of the imagina- 
tion, as he does also Darwin's hypothesis of a pri- 
mordial germ as the source of all the variety of 
organisms now upon the earth's surface. These in- 
stances, and many others that are among the most 
brilliant achievements of science, lead us to look 
upon the imagination as itself an instrument of 
observation, and in the form of carefully stated 
hypothesis, it leads to an explanation of many ob- 



SOME EXPLANATORY METHODS OF INDUCTION 427 

served facts which without its aid would postpone 
indefinitely important lines of research. 

Verification of Hypotheses. If we are to carry 
our explanations of events to a successful termina- 
tion, the hypotheses by means of which the rela- 
tions of particular phenomena are brought under an 
intelligible view need to be tested and not merely 
stated, to be verified, not merely formulated. There 
are two steps in the process of verification to which 
we may give attention. "To prove or disprove (an) 
induction we must have resort," says Tyndall, "to 
deduction and experiment." Mill's definition of an 
hypothesis, that it is "any supposition which we 
make (either without actual evidence, or on evidence 
avowedly insufficient) in order to endeavour to 
deduce from it conclusions in accordance with facts 
known to be real," points to the same two require- 
ments. An hypothesis which is not capable of be- 
ing verified would serve no immediate purpose, and 
whether it serves any purpose at all need not con- 
cern us. We are now studying living hypotheses, 
those which answer questions, and render intelli- 
gible the particular facts of observation. And it is 
about these that we are warned that it is not their 
intelligibility merely, and not the fact that they 
answer questions, which recommends them finally to 
our acceptance. It is only if our hypotheses are 
true, if they make us acquainted with the actual 
relations which objects sustain to one another, that 
they are received as part of our scientific knowledge. 
The formation of hypotheses takes us beyond what 



428 A TEXT-BOOK OF LOGIC 

is actually known and observed, and for this reason 
there is in every hypothesis an element of risk; but 
they must at the same time make it possible for us 
to return to fact and the observation of fact, and it 
is this that renders them useful in the advancement 
of human knowledge. The return to fact is made 
in the two steps of deduction and experiment. 

Let us take as an illustration of these two stages 
in the process of verification the well-known fact 
that water rises to a certain height in a pump, and 
the explanation of this fact on the ground that 
"Nature abhors a vacuum." The story goes that in 
trying to raise water to a great elevation, some 
Florentine gardeners found that the column of 
water ceased at the height of thirty-two feet. The 
matter was referred to Galileo who, embittered by 
the reception that had been accorded to his science, 
said that he supposed that Nature abhorred a 
vacuum only at the height of thirty-two feet. It 
was left for Toricelli, Galileo's pupil, to provide an 
answer to the inquiry. He supposed that water 
might be forced into a tube by pressure on the sur- 
face of the liquid outside. After much thought, it 
occurred to Toricelli that the atmosphere might 
exert such pressure, and that the column of water 
thirty-two feet in height might be the exact weight 
necessary to equalise this atmospheric pressure. 
This supposition was Toricelli's hypothesis. Was it 
true? This was the next question that the physicist 
confronted, and it is exceedingly instructive to ob- 
serve the way he went to work to verify his hypoth- 



SOME EXPLANATORY METHODS OF INDUCTION 429 

esis. He deduced certain consequences from the 
hypothesis. He argued that if thirty-two feet of 
water will hold the atmospheric pressure in equili- 
brium, a shorter column of a heavier liquid should do 
the same. According to his calculations, mercury, 
which is thirteen times heavier than water, should 
be able to balance the pressure of the atmosphere 
at thirty inches. The next step in the process of 
verifying the original hypothesis was an experi- 
ment. Toricelli filled a glass tube a yard or so in 
length, open at one end and closed at the other, 
with mercury. Placing his thumb over the open 
end, he inverted it in a bath filled with the same 
metal. When he removed his thumb, the mercury 
began to sink, and continued to sink until the height 
of thirty inches had been reached. The proof of the 
hypothesis was complete. 

Hypothesis and Theory. The difference between 
an hypothesis and a theory is a relative one merely. 
To bring out this feature of the terms' meanings, 
we may say that a theory is a completely verified 
hypothesis, and that an hypothesis is an incom- 
pletely verified theory. This statement will have 
served its purpose if it remind us that hypothesis and 
theory both spring out of the demand for explana- 
tion, that they both involve the use of the creative 
imagination for their formation, and call for verifi- 
cation in the way that has been described. It is these 
similarities which justifies the popular use of the 
terms as synonymous. It will be useful for us, how- 
ever, to look at the matter a little more closely. We 



430 A TEXT-BOOK OF LOGIC 

may observe, for instance, that we advance from 
hypothesis to theory, not by leaving our hypothesis 
behind, but by developing it in the light of further 
experiences so as to make it accord with facts hith- 
erto not known or not understood. In this sense, the 
hypothesis becomes a theory. To illustrate, when ice- 
cold water is poured into a glass on a hot summer 
day, little drops of water collect and trickle down on 
the outside of the glass. How do we account for this 
phenomenon ? The sudden cooling of the glass takes 
place by radiation of its heat, and the water-vapour 
of the atmosphere condenses on the cooled surface 
of the glass. The same hypothesis may be extended 
to account for the formation of dew, and a number 
of other phenomena. An hypothesis that can be 
used to explain a variety of facts which were not 
thought of when the hypothesis was formulated, can 
justly be regarded with greater confidence than one 
which explains only a single phenomenon. Every 
new fact which fits into an hypothesis strengthens 
it. At first, an hypothesis has an explanatory value 
only for the particular phenomenon with respect to 
which it is framed. But if an hypothesis is ca- 
pable of growth, both in respect to the number and 
variety of the facts which it is capable of explain- 
ing, and in the simplicity of the form which it as- 
sumes, the conditions are present for the develop- 
ment of the hypothesis into what is known as a 
theory. We speak, for example, of the Darwinian 
hypothesis, because the supposition it states is still 
in a condition of growth, and because the modifica- 
tions which are being introduced into Darwin's 






SOME EXPLANATORY METHODS OF INDUCTION 431 

statement are intended to make his view harmonise 
more fully with progressive experience and recent 
discovery. When, however, we regard the idea of 
growth throughout the known world as a confirmed 
doctrine of science, we no longer speak of the Dar- 
winian hypothesis, but of the theory of evolution. 
In the same way, and for similar reasons, we speak 
of the theory of gravitation, the Copernican theory, 
the theory of the conservation of energy. What 
we mean by such designations is that the evidence 
for the particular hypotheses which lies back of 
them is ample and varied, that the exceptions within 
the fields of their application are either insignficant 
or are absent altogether, that newer experiences 
and discoveries tend to confirm these views. When 
lines of evidence tend to converge and to be focussed 
on an hypothesis, that hypothesis has no longer the 
tentative position of a supposition, but the firmer 
and surer foundation of a confirmed belief. The 
formulation of such a confirmed belief is called a 

theory. 

REFERENCES 

H. A. Aikins, The Principles of Logic, Ch. XXV. 

B. Bosanquet, The Essentials of Logic, Lecture X., Ch. I., 

e-b, 3. 
J, E. Creighton, An Introductory Logic, 3d Edition, Chs. 

XIV., XV., XVIII., XIX. 
J. G. Hibben, Logic Deductive and Inductive, Part II., Chs. 

IIIc, XL, XII., XIII., XIV. 
W. S. Jevons, Elementary Lessons in Logic, Lessons XXVI., 

XXVII. 
S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
tion, Ch. VIII., §§ 4-8. 



432 A TEXT-BOOK OF LOGIC ; 

W. Minto, Logic, Inductive and Deductive, Chs. IX., X. 

C. Read, Logic, Deductive and Inductive, 3d Edition, Chs. 

XV., §§ 5-7, XVIIL, XIX., XX. 
W. J. Taylor, Elementary Logic, Chs. XV., XVI. 

ADVANCED 

B. Bosanquet, Logic, Vol. II., Book II., Chs. II., III., IV., V. 
W. R. B. Gibson, The Problem of Logic, Chs. XXXVIII., 

XLII. 
W. S. Jevons, The Principles, of Science, Chs. XVIIL, XIX., 

XXIIL, XXIV., XXVL, XXVIL, XVIIL 
H. W. B. Joseph, An Introduction to Logic, Ch. XXL 
H. Lotze, Logic, Vol. II., Book II., Chs. VIII., IX. 
J. S. Mill, A System of Logic, Book III., Chs. VII., XIV., 

XX., XXIIL 
F. C. S. Schiller, Formal Logic, Chs. XIX., XXII. 
J. Venn, Empirical Logic, Chs. XVI., XXI. 
J. Welton, A Manual of Logic, Vol. II., Book V., Chs. III., 

§§ 147, 149, IV., V., §§ 153, 154, VII. 

QUESTIONS 

1. Is there necessarily any irreconcilable opposition be- 
tween the view that the aim of science is complete ob- 
servation, and that it is explanation? Explain. 

2. To what simple type does all scientific explanation con- 
form? Illustrate. 

3. What is meant by saying that explanation consists in 
discovering the conditions of the occurrence of phe- 
nomena? 

4. Are all the circumstances attending the occurrence of 
an event conditions of its occurrence? 

5. What is meant by saying that the phenomena of ob- 
servation and those of explanation are continuous with 
each other? 

6. What bearing, if any, do the facts included in your 
answer to the previous question have upon the dis- 
tinction between a phenomenon and its conditions? 



SOME EXPLANATORY METHODS OF INDUCTION 433 

7. In what sense can it be said that scientific explanation 
is a process by which what is given in observation is 
supplemented by what is not so given? 

8. Can you connect the conception of scientific explanation 
implied in the previous question with the conception of 
knowledge stated in Chapter I? 

9. State and illustrate three senses in which the word 
analogy is used. 

10. Why is not any kind or degree of resemblance a safe 
principle of inference? 

11. What is meant when it is said that analogical reasoning 
depends upon important resemblances? 

12. In what way does the validity of reasoning by analogy 
depend upon the attitude one takes toward differences? 

13. What light does the saying that analogy 'sticks in the 
particular instances' throw upon the character of ana- 
logical argument? 

14. In what sense can analogy be regarded as a method of 
explanation? 

15. What are the limits of analogical argument? 

16. What does Mill mean by calling analogy 'a. mere sign 
post'? 

17. State and illustrate what you understand by an hypoth- 
esis. 

18. Why must hypotheses be stated in terms of the same 
order as the phenomena they attempt to explain? 

19. Is there any objection against calling hypotheses 
'guesses,' and, if so, what is the ground on which it 
rests? 

20. What reason may be given for the scientists' objection 
to the use of hypotheses? 

21. What is the relation of imagination to the task of for- 
mulating scientific hypotheses? 

22. What are some of the 'facts' which we owe to the 
exercise of imagination in the field of the natural 
sciences? 

28 



434 A TEXT-BOOK OF LOGIC 

23. State and explain the two steps involved in the veri- 
fication of hypotheses? 

24. Illustrate by the use of concrete example the process 
of verifying an hypothesis. 

25. How do hypothesis and theory agree with and differ 
from each other? Illustrate. 

EXERCISES 

1. Examine the explanations of three simple events with 
which you are acquainted, and state whether they con- 
form or not to the fundamental form of explanation 
as stated in the text. 

2. Give three instances in which explanation consists in the 
statement of the conditions of a phenomenon's occur- 
rence. 

3. Give two llustrations, one from literature and one from 
science, of analogy. Examine each with a view to show- 
ing to which meaning of the word it conforms, and 
whether it satisfies the conditions of a valid inference. 

4. Upon what logical principle does each of the following 
statements depend, and what can you say as to their 
validity as arguments: 

(1) It is said that a general resemblance of the hills 
near Ballarat in Australia to the California hills 

where gold had been found suggested the idea of 
digging for gold at Ballarat. 

(2) There are no great nations of antiquity but have 
fallen to the hand of time; and England must join 
them to complete the analogy of the ages. Like 
them she has grown from a birth-time of weakness 
tutelage to a day of manhood and supremacy, but 
she has to face her setting. Everything that 
grows must also decay. 

5. Construct an hypothesis to explain some fact of your 
experience, and explain how it may be verified or over- 
thrown, 



CHAPTER XVI 

CAUSATION 

General Statement of the Problem. The fact that 
underlies the problem of causation is the observed 
regularity in the order of the particular phenomena 
which occur in the course of our ordinary expe- 
rience, and in the fields of the several sciences. 
That our ordinary and scientific experience is char- 
acterised, within ascertainable limits, by some kinds 
and degrees of regularity is a fact about which 
there is universal agreement. Indeed, this is a fea- 
ture of experience so generally recognised that it 
constitutes the starting point not only of the theo- 
retical interest which leads us to the more accurate 
forms of human knowledge, but also of the practical 
interests which lie at the foundation of the political, 
commercial, and social relations by which human 
individuals are held together in a community. A 
world from which all order were absent would be a 
world in which all thought and action would be im- 
possible, and to which all thinking and active agents 
would ultimately succumb. The institutions of 
society and the organisation of the sciences pre- 
supposes that some sort of unity and order belong 
to the world ; and it is the business of all our sciences 
to study the regularities of the phenomena and 
events of the world for the purpose of endowing 
our notion of such regularities with greater pre- 

(435) 



436 A TEXT-BOOK OF LOGIC 

cision. The problem, then, that confronts us in view 
of this regularity of the world's order is : How shall 
we conceive this regularity so as to make intelligible 
to ourselves the principles or laws by which it is 
maintained and upon which it depends? 

The Practical Aspect of the Question. There is 
no doubt that this is not a theoretical question 
merely, a question only of the sciences, and unim- 
portant or superfluous in the absence of theoretical 
interests. The way in which the world in which 
we live may be expected to behave is a broadly 
practical interest; and the man who in the morning 
starts off to his office, as well as the one who goes to 
his laboratory, begins the day's work with the ex- 
pectation that the uniformities upon which he has 
relied in the past will be maintained in the present. 
Indeed, we may say that, in the history of the indi- 
vidual and of the race, interest in the regularity 
of the course of observed events was practical before 
it was theoretical; and it would not be difficult to 
show that the practical motive has never been 
divorced from the theoretical when, in the progress 
of the sciences, these uniformities have become 
the subject of very specialised study. No one, 
for instance, who has the least knowledge of 
primitive peoples can fail to be impressed with the 
fact that the origin and development of their insti- 
tutions is closely interwoven with their struggle 
with the forces of nature. Upon his understanding 
of the physical world has depended the primitive 
man's ability to maintain himself in existence. We 



CAUSATION 437 

see the relationship thus indicated between the 
growth of intelligence and the economic struggle 
illustrated in a broad way if we contrast, for ex- 
ample, the peoples of the northern and southern 
latitudes. Whenever, as in the latter case, the food 
supply is plentiful and relatively independent of the 
cultivation of the domestic arts, intelligence is com- 
paratively low ; but when, as in the former case, the 
food supply is scanty or precarious, it becomes 
increasingly important to understand the physical 
environment from which has to be won the means 
of physical support, and, if the community is to 
perpetuate itself, to socialise this knowledge in the 
domestic arts. 

There are many concrete illustrations of the 
way in which, at the present time, observation 
of natural occurrences, and inferences drawn from 
such observation, are allowed to affect our prac- 
tical life. From the character of the sunset 
we infer that it will be a fair or stormy day to- 
morrow, and, therefore, that it will, or will not, be 
possible to take a day's outing in the country. What 
the farmer calls 'good growing weather' is an infer- 
ence, based upon observed connections in the past, 
of the same practical sort. Now about the facts that 
underlie such practical inferences as these, we may 
observe that they are selected, often by the cooper- 
ative labours of many generations of observant men, 
from a very complex mass of details, and that no 
effort is made, as a rule, either to determine the pre- 
cise nature and connection of the facts themselves, 



438 A TEXT-BOOK OF LOGIC 

or to enumerate exhaustively the other factors with 
which, in our experience, they are associated. For 
example, what constitutes 'good growing weather' 
may be for one man a matter of temperature, for 
another a matter of humidity, and for a third a 
matter of both ; but neither of these factors, nor both 
together, can be regarded as a sufficient explanation 
of the term, and many other elements of the situ- 
ation in which it is relevant to talk about growing 
weather must be taken account of — such, for in- 
stance, as the nature of the particular crop, the 
particular stage of its growth, its condition at that 
stage, the nature of the soil, the location of the field 
in which the crop is growing, etc. — if the phrase 
is to have for us any practical significance. When, 
therefore, we examine the character of those uni- 
formities which our practical interests lead us to 
observe, we find that they are made up of certain 
striking or important features of a complex situ- 
ation, which are connected together in such a way 
that, on their recurrence in our experience, we are 
led to expect the recurrence of other features of the 
situation with which they have been associated in 
our past experience. In other words, one part of 
an experience is taken as a sign of the recurrence 
of another part with which it is usually connected. 
Beyond such empirical connections as are found in 
experience, the practical view of causation does not 
enable us to advance. 

The Theoretical Aspect of the Question. If we 
compare the theoretical with the practical way of 



CAUSATION 439 

dealing with the observed regularities in the occur- 
rence of natural events, we shall see that it differs 
from the latter in two respects. In the first place, 
the theoretical view, in Venn's suggestive phrase, 
'screws up' the antecedent or cause and the conse- 
quent or effect of an event into close juxtaposition, 
so that they come to be regarded as nearly as pos- 
sible concurrent. The possibility of doing this, it is 
obvious, depends upon our ability to eliminate from 
the phenomenon we are examining all the disturb- 
ing or irrelevant elements. If, therefore, it is re- 
membered that no two natural events are exactly 
alike in all their details, that some of the attendant 
circumstances are peculiar to the instance of the 
phenomenon we are examining, and form no part of 
the phenomenon itself, it is evident that the omission 
of these, by whatever means it is brought about, 
can serve only to give greater precision to the fac- 
tors that are involved in the orderly sequence, and 
to make it possible to determine with greater accu- 
racy the details which are involved in the causal 
relation. We pass from the practical to the more 
theoretical view of causation, that is to say, when 
we devise means of eliminating from our observa- 
tion of natural events what is irrelevant to our 
search for the conditions of the occurrence of such 
events. 

In the second place, the theoretical view insists 
upon the importance of a careful analysis of the 
antecedents of an event as a condition of establish- 
ing a causal relation. Mill insisted on this point 



440 A TEXT-BOOK OF LOGIC 

with some emphasis, and he criticised the practical 
view for the unregulated way in which it picks out 
some one event or circumstance, and calls it the 
cause. There is just ground for Mill's contention, 
if our study of the observed regularities in the 
occurrences of natural phenomena is made from 
the point of view of the requirements of accu- 
rate knowledge; but if we admit the legitimacy of 
the practical point of view, if, that is, the order of 
nature's changes are taken as a clue to the kinds of 
conduct that are likely to be efficient, we may say 
that the more refined analysis that Mill had in mind, 
and which is required by science, would in large 
measure defeat this latter purpose. It is because 
the interests of science are so intimately bound up 
with a detailed knowledge of the conditions of phe- 
nominal occurrences that, in contrast with those of 
the practical life, its requirements are satisfied only 
by the minute analysis of the phenomena with which 
it is particularly concerned. In emphasising this 
point Mill has directed attention to an important 
difference between the practical and theoretical 
views of the causal relation. 

The Genetic Relation of the Practical and Theo- 
retical Views. While the theoretical view of caus- 
ation differs, as we have said, from the practical in 
important respects, we should be departing from 
the truth if we supposed that the differences between 
these views expressed the whole truth about them. 
There is between the two views no such opposition 
in fact as an examination of their differences alone 



CAUSATION 441 

would lead one to think. We must regard them, 
rather, as earlier and later stages in the progressive 
efforts of the race to make clear to itself the rela- 
tion in which it stands to the changing environment 
under which its life has to be lived. It was doubt- 
less useful for the theoretical view that practical 
interests had led to the observation of large numbers 
of uniformity in the occurrence of natural events. 
In this way, material was already prepared for it, 
and to this material it could apply the stricter 
methods which a change in interests was the means 
of defining. But in developing and applying these 
methods the sciences have not freed themselves alto- 
gether from practical considerations and, moreover, 
have themselves contributed very largely toward a 
new and broader conception of the practical itself. 
By this statement we do not merely mean that, in its 
history, scientific progress frequently has been 
determined by difficulties encountered in a narrowly 
practical way, nor merely that scientific truth has 
so often been found capable of a like practical 
application; the more important fact is that, as 
scientific aims and methods have become established, 
our conception of what is practical has been broad- 
ened to include any kind of activity that is directed 
toward the attainment of an end. In the sense in 
which nowadays we use the word, any regulated or 
consciously controlled process is practical, and it 
would seem that science has not only contributed to 
this conception but is itself, in this meaning of the 
term, preeminently a practical affair. And just be- 



442 A TEXT-BOOK OF LOGIC 

cause the scientific man approaches his problems 
with definite questions in his mind, because, as 
Bacon said, he interrogates nature, there is a limit 
set, by the nature of the questions themselves, to 
the amount of analysis that is necessary in arriving 
at the solution of particular problems. It is not, 
therefore, in the amount of analysis performed that 
we can find the distinguishing mark of a theoretical 
view of the causal question. For if we insist that 
our analysis in any field whatever must be relevant, 
in kind and amount, to the purpose for which it is 
undertaken, it becomes at once obvious that the 
practical and theoretical views are brought together 
under a single view, and that the differences enu- 
merated above must be understood, not as placing 
the views in question in different classes, but as indi- 
cating different species of activity which belong to a 
single class. 

The Origin and Nature of the Causal Problem. 
In view of the foregoing considerations, two facts 
may be said to be fairly well established. In the 
first place, there is good reason for believing that 
the causal problem arises from the importance that 
the presence of order in human experience has for 
the practical no less than for the theoretical life. 
The problem of causation is of such general interest, 
as we have seen, not because the world in which 
we live is unregulated and disordered, but because, 
being regulated and ordered, we can adjust our- 
selves to it better if we know the principles and 
laws according to which, in the future as in the 



CAUSATION 443 

past, things and events may be expected to happen. 
It is well to be perfectly clear on this point, because 
frequently its neglect has led to a somewhat one- 
sided, if not misleading, view of the problem itself. 
We have called attention to the impossibility of 
considering the causal problem as in any essential 
respect different for the scientist than for the prac- 
tical man. For both, it is the fact that experience 
presents us with certain regularities in the order 
of our experience that directs attention to the prob- 
lem, and that leads to a study of these regularities. 
We do not study the causal problem, that is to say, 
to escape from a world of chaos to a world of order, 
but, starting with the world of order, we seek to 
understand its laws, and to ascertain how far these 
laws are capable of being extended to new and 
larger areas of life. 

In the second place, it is clear that the problem 
of causation has nothing whatever to do with the 
question why things happen as they do, if by that 
question is meant an inquiry into the reasons why 
our experience has the distinctive characteristics 
that it is known to have. Science, and the same 
thing is equally true of philosophy, starts with the 
acceptance of the world as it is known in human 
experience, a world, as we have seen, that has a cer- 
tain determinate character. Now about such a world, 
it would be futile to ask ourselves why it has this 
rather than some other character, since the very 
problems which confront us in our everyday life, and 
in our sciences and philosophy as well, arise out 



444 A TEXT-BOOK OF LOGIC 

of the world's character as made known by human 
observation. The facts about the world in which 
we live, as these are observed and reported in in- 
creasing numbers and with improving accuracy, 
constitute the material of all human knowledge, and 
if there are any further questions that arise, these 
must concern the way in which such facts are con- 
nected in the unity of an ordered system. Instead, 
therefore, of conceiving the causal problem as an 
inquiry into the reason why facts are what they 
are, we must view it rather as demanding of us an 
exposition of the nature of the connection that binds 
the various parts of human experience together. 
Put simply, the causal problem is concerned, not 
with the question why things are what they are, 
but with the question how things happen as they 
do. 

The Course of Our Further Discussion. Our fur- 
ther study of the causal problem will bring before 
us particularly three closely related questions. We 
shall examine, in the first place, the time relations 
of causal events; in the second place, the complex 
character of such events will demand attention; 
and in the third place, we must try to make clear 
what is meant by the necessity that is always recog- 
nised as belonging to such events. In our discussion 
of each of these topics, we shall make MilPs treat- 
ment, in Book III., Chapter V., of the Logic, our 
point of departure. It will be advantageous, there- 
fore, for the student to read the whole of Mill's 



CAUSATION 445 

chapter in connection with the following para- 
graphs. 

The Time Relations of Causal Events. The first 
characteristic of a causal relation that Mill enu- 
merates is the 'invariable antecedence' of certain of 
the factors involved in the causal relation. He says 
that "invariability of succession is found by observa- 
tion to obtain between every fact in nature and 
some other fact which preceded it. . . . The 
invariable antecedent is termed the cause; the in- 
variable consequent, the effect. And the universal 
law of causation consists in this, that every conse- 
quent is connected in this manner with some ante- 
cedent or set of antecedents. . . . For every event 
there exists some combination of objects or events, 
some given concurrence of circumstances, positive 
and negative, the occurrence of which is always 
followed by that phenomenon." He points out that 
we may not have discovered what the particular 
concurrence of circumstances may be in a given 
case, "but," he adds, "we never doubt that there is 
such a one, and that it never occurs without having 
the phenomenon in question as its effect or conse- 
quence." 

In this passage, Mill definitely raises the ques- 
tion of the time relations of causal events. In lay- 
ing emphasis on the antecedence of the cause, Mill 
takes the view that for any event to be considered 
as a cause at all, it must exist in time before the 
event which is, or may be regarded as, its effect. 
This, doubtless, is the conception of the time rela- 



446 A TEXT-BOOK OF LOGIC 

tions of cause and effect that prevails generally at 
the present day, and it may be worth while to ask 
how far it is an accurate description of the facts 
that are involved in causal events. There are, 
without question, many examples of the causal rela- 
tion that lend themselves quite naturally and easily 
to this interpretation, examples, that is to say, in 
which the fact that we call the cause and the fact 
that we call the effect appear to be temporally dis- 
tinct events. A blow on the head, for instance, may 
be followed by the loss of consciousness, and 
may be said to be the cause of the loss of con- 
sciousness. The explosion of a powder magazine 
may follow the application of a lighted match or 
fuse to the powder. Diphtheria makes its appear- 
ance ten days after the ingestion of the Klebs- 
Loefner bacillus which, the physicians tell us, is the 
cause of the disease. In all these cases we have, or 
seem to have, undoubted examples of the necessary 
temporal priority of the cause, and the necessary 
posteriority of the effect, in causally related phe- 
nomena. It may be doubted, however, whether all 
causally related events can be made to fall so easily 
and naturally within this scheme or view. It would 
be difficult, for example, to detect in the explanation 
offered by the chemist of the formation of rust the 
temporal discontinuity of cause and effect which is 
an essential part of Mill's doctrine of causation. 
Rust formation, so we are told, is due to the combi- 
nation of iron with the free oxygen of the air ; but, 
if that is so, it is quite obvious that the chemical 



CAUSATION 447 

combination of oxygen and iron does not precede, 
but is contemporaneous with, the formation of rust 
itself. There are innumerable instances of a similar 
character, and we may even say that the example 
chosen is typical of most of the chemical processes 
with which we are at all familiar. The case is im- 
portant because of the large field of application of 
chemical laws, not only in the inorganic, but in the 
organic world as well. To take only one such 
example, we now know that bacterial action is 
largely, if not wholly, due to the toxins generated 
by microscopic organisms; and, if that is true, the 
final explanation of their action and results is, as 
is coming to be seen, a highly specialised branch of 
the science of chemistry. If, as seems probable, the 
results of bacterial action are not separable in time 
from the production of their toxins, an overwhelm- 
ing list of examples can be appealed to to throw 
doubt on the necessary temporal antecedence and 
consequence of the events involved in the causal 
relation. 

It is owing to some such considerations as these 
that the position has sometimes been taken that 
there is no distinction whatever between the cause 
and the effect of a phenomenon, in other words, 
that the cause and effect are identical. There seems 
no sufficient reason in the nature of causal phe- 
nomena why we should adopt so paradoxical a view. 
Cause and effect do stand for distinct things in our 
experience of causal events, and if, as we have said, 
this distinction is not necessarily one of temporal 



448 A TEXT-BOOK OF LOGIC 

discontinuity, we need to inquire further what the 
distinction is. 

When we say that the relation of cause and 
effect is not necessarily one of antecedence and 
consequence in time, we must not be understood to 
affirm that causal phenomena have no relation at 
all to time. That would be not only a paradox, but 
exceedingly difficult to maintain. It is no doubt 
true that all causal phenomena are events in time, 
that they are constituted by a number of facts 
which come before and after one another in a series. 
That the whole number of facts in a causal phe- 
nomenon have a definite sequence and order in time 
there is no need to deny, and that the order and 
sequence can be determined is the permanent ex- 
pectation and belief of science. From this fact, 
however, it does not follow that, within the series, 
the cause and effect are separated by a necessary tem- 
poral interval. What rather we seem warranted 
in saying with respect to the causal series is that 
their factors are continuous, — temporal continuity, 
not temporal discontinuity, seems to be the charac- 
teristic of all such events. But whether within the 
causal series the cause antedates the effect, or is 
contemporaneous, at least in part, with it, as it 
must be, for example, in the circular reactions of 
chemistry, is a fact to be determined in the par- 
ticular instance. But whatever may be true of any 
particular instance, temporal discontinunity cannot 
be regarded as an essential feature of the causal 
relation. The utmost that we can say, from the 



CAUSATION 449 

standpoint of their temporal relations, is that the 
cause and effect are continuous with one another. 

The Complex Character of Causal Events. It is 
seldom, if ever, according to Mill, that an invariable 
sequence subsists between a consequent and a single 
antecedent. Usually, the causal relation exists 
between "a consequent and the sum of several ante- 
cedents ; the concurrence of all of them being requi- 
site to produce, that is, to be certain of being fol- 
lowed by, the consequent." If, for example, "a per- 
son eats of a particular dish and dies in consequence, 
that is, would not have died if he had not eaten of 
it," the death is usually attributed to eating of the 
dish although, as Mill points out, there were other 
factors contributing to the result, such as the bodily 
constitution of the individual, the particular state 
of his health, and, perhaps, a certain state of the 
atmosphere. These taken in conjunction with eat- 
ing of the dish are, according to Mill's view, the 
'invariable antecedent.' When we select one among 
the antecedents of a phenomenon and call this the 
cause, our selection, Mill says, falls generally on 
the one which came last into existence. But, he also 
points out, there is hardly any one among the num- 
ber of antecedents that may not serve in this special 
sense as the cause "according to the purpose of our 
immediate discourse." This tendency "to associate 
the idea of causation with the proximate antece- 
dent event, rather than with any of the antecedent 
states, or permanent facts, which may happen also 

29 



450 A TEXT-BOOK OF LOGIC 

to be conditions of the phenomenon," Mill regards 
as not at all necessary to the common notion of 
cause. The conclusion, then, at which he arrives 
is that by a cause is meant "the sum total of the 
conditions, positive and negative, taken together; 
the whole of the contingencies of every description 
which being realised, the consequent invariably fol- 
lows. The negative conditions . . . may be all 
summed up under one head, namely, the absence 
of preventing or counteracting causes." 

The essential contentions of Mill in this passage 
are, first, that the antecedent of any fact is a com- 
plex group of facts, and, second, that the cause, 
popularly considered, is taken to be some one fact 
among the antecedents selected arbitrarily or for 
some special purpose. With regard to the first 
point we may quote Jevons. He says : "By an ante- 
cedent we mean any thing, condition, or circum- 
stance which exists before or, it may be, at the same 
time with an event or phenomenon. By a conse- 
quent we mean any thing, circumstance, event, or 
phenomenon, which is different from any of the 
antecedents and follows after their conjunction or 
putting together. It does not follow that an ante- 
cedent is a cause, for the effect might have hap- 
pened without it. Thus the sun's light may be an 
antecedent to the burning of a house, but not the 
cause, because the house would burn equally well 
in the night ; but a necessary or indispensable ante- 
cedent is identical with a cause, being that without 
which the event would not take place. . . . There 



CAUSATION 451 

are usually many different things, conditions, or 
circumstances necessary to the production of an 
effect, and all of them must be considered causes 
or necessary parts of the cause. Thus the cause 
of the loud explosion in a gun is not simply the 
pulling of the trigger, which is only the last appar- 
ent cause or occasion of the explosion ; the qualities 
of the powder, the proper form of the barrel, the 
proper arrangement of the percussion-cap and pow- 
der, the existence of the surrounding atmosphere, 
are among the circumstances necessary to the loud 
report of a gun ; any of them being absent it would 
not have occurred." In this passage it may be 
observed that what is popularly regarded as the 
cause, the second point mentioned by Mill, Jevons 
calls the occasion of the event, that is, that which, 
in connection with the other necessary antecedent 
or coexisting conditions, is effective in bringing 
these latter into active operation. What Jevons 
here speaks of as the occasion is sometimes called 
the immediate cause, the other necessary attendant 
circumstances being referred to as the conditions 
or causal conditions of the event in question. 

That the cause of any event is some complex 
group of facts or circumstances is undoubtedly true. 
Indeed, this seems to follow as a matter of necessity 
from the general character of human experience. 
As we have pointed out frequently, objects and 
events are experienced by us, not as separate and 
individual things, but as subsisting with other ob- 
jects and events with which they are connected in 



452 A TEXT-BOOK OF LOGIC 

a variety of ways. It is this feature of experience 
that was said above to be the starting point of the 
casual problem. Now it is no doubt true that within 
any experienced complex we can, and in fact do, 
isolate, by an act of discriminative attention, a 
given fact or event which we regard, for reasons 
special to the case, as the effect or result of other 
perceived or discoverable facts, and that, in this 
way, a certain uniqueness, a certain independence, 
comes to be regarded as the distinguishing mark of 
all effects whatever. But while no objection can be 
brought against thus isolating an effect, since in this 
way it is rendered more capable of exact descrip- 
tion, and the particular causal relation that has to 
be determined is made more capable of exact defi- 
nition, a similar line of remark does not apply to 
what we understand as a cause. For, in the first 
place, it is only because what we call the effect 
has a definite character that the search for a cause 
becomes a problem at all. Unless the fact or event 
of which we wished an explanation were made 
definite, there would be no point of starting for the 
establishment of a causal relation. It is owing to 
the fact that some part of the experience of which 
the effect is only a fragment remains indefinite that 
the cause is characterised at first by an indeter- 
mmateness that would be quite fatal if it attached 
to the effect. 

But, not to press this point, we cannot be 
sure, in the second place, that, in any particular 
ease, all the conditions which will make the oc- 



CAUSATION 453 

currence of an effect intelligible fall within our 
experience of that case. As we have seen above, 
experimental and theoretical observation are val- 
uable chiefly because they bring within experience 
factors, material to our understanding of a phe- 
nomenon, that are not included in our ordinary 
perception of it. An example, usually cited, is the 
discovery of the planet Neptune by Galileo in 1846. 
The observed fact which led to its discovery was the 
deviation of the planet Uranus from the course 
determined for it by the attractive forces of the 
sun, Jupiter, and Saturn. It was suggested, first 
by Adams and later by LeVerrier, that this devia- 
tion could be accounted for if we supposed that 
some hitherto unknown body, situated external to 
it in a particular position and at a given distance, 
were affecting the movement of the planet. Such 
a body, situated where Adams and LeVerrier had 
suggested, was later discovered by Galileo, and 
exists in our solar system as the planet Neptune. 
In the third place, we may observe that, whether 
all the factors necessary to a causal relation are or 
are not parts of our ordinary perception of it, as 
indeed the illustration just used is sufficient to show, 
the effectiveness of any given fact, — the planet 
Neptune, for example, — seems to depend as much 
on its relations to other facts, — the sun, Jupiter 
and Saturn, — as it does on its own existence. It 
is no doubt true that if the fact, — the planet Nep- 
tune, — did not exist, it could be neither a cause 
nor any part of a cause ; but if it is a cause or part 



454 A TEXT-BOOK OF LOGIC 

of a cause at all, it owes this character, not merely 
to its existence, but also to the way it acts and is 
acted upon by other facts in the system of facts in 
which the effect, — the course of Uranus, — is in- 
cluded as an important, and, indeed, a necessary ele- 
ment. To take another illustration, we cannot re- 
gard death as the result of a gun shot, poison, or 
any other single fact, but as the result of a net- 
work of facts which includes the gun shot or what 
not in a system which extends to and embraces the 
stated effect. From this point of view, it is evident 
that the problem of causation is one in which, start- 
ing with some fact or event, we endeavour to build 
up by observation and experiment a system of facts 
within which the fact or event with which we 
started is necessarily included. Causes, conse- 
quently, must always be complex, and the difficulty 
of determining causes is the difficulty of including 
within the system only those factors that are mate- 
rial to it. 

Few words are necessary to make our position 
clear on the second point raised by Mill, namely, the 
importance usually given to one of the conditions 
of an event and naming this the cause. Prac- 
tically, as Mill pointed out, the fact selected is 
usually the one which is nearest in time to the effect. 
But, as we have seen, the immediate temporal ante- 
cedence of the cause is not necessarily an essential 
feature of the causal relation. What rather, even for 
the practical view, is needed is the selection of an 
agent on which reliance can be placed to bring about 



CAUSATION 455 

the desired result. Certainty as to the cause seems 
to be the desideratum, whether the causal factor is 
the immediate temporal antecedent of the effect or 
not. When, for example, we wish to rid the prem- 
ises of rats, to borrow an illustration, we may- 
choose either traps, strychnine, phosphorus, or ter- 
riers, and doubtless the one selected will be the one 
that, under the circumstances, is regarded as most 
efficient. And by efficient, in this connection, we 
mean the one that, with due regard to the circum- 
stances of the case, realises best the purpose for 
which it is chosen. Now when the purposes, for 
the satisfaction of which causal relations are sought, 
become specialised as they do in science, when, 
that is, they are directed toward the attainment of 
knowledge, and not toward the improvement of the 
material conditions of life, the situation, so far as 
the causal relation is concerned, is not greatly dif- 
ferent, for in science the search for a cause is 
determined by a purpose which the ascertainment 
of the cause itself is expected to satisfy. In the 
field of science, as was pointed out before, the pur- 
pose that directs an inquiry does not lie outside of, 
but is one with, the attainment of scientific truth. 
In this the chief difference between the theoretical 
and practical life is to be found. But when we have 
said that, it remains true that the conditions of 
knowledge are more rigid than those of practice, 
and the goal of inquiry requires more strict defini- 
tion. Hence we find that what passes for a cause in 
practical life may seem, from the scientific point of 



456 A TEXT-BOOK OF LOGIC 

view, altogether inadequate, if not false, and, con- 
sequently, that a more thorough analysis of the 
antecedent and concurrent circumstances has to be 
undertaken if the end of scientific truth is to be 
reached. Now, whether or not, for the purpose of 
science, all or only part of the circumstances and 
conditions of an event are included in its cause will 
depend on the particular and immediate purpose it 
is intended to satisfy. No doubt, the ultimate goal 
of science is to discover laws of connection which 
are capable of extension to other than the observed 
phenomena, but, at the same time, we should observe 
that it can reach this end only by the determination 
of the particular connections of one empirical event 
with another in human experience. But even in 
this more restricted field of scientific effort, a cer- 
tain rigid demand is usually made and observed, 
namely, that all and only those factors which can 
be regarded as essential conditions of a fact or 
event should be enumerated as its cause. It is only 
when there is a lapse from strict scientific precision 
that any thing less is possible ; and even when such 
lapse takes place, the scientist feels himself obliged 
to fill out, on demand, the scantier statement by 
restoring all the enumerated elements that are of 
material importance to our understanding of the 
case. 

The Necessity of Causal Events. The two fac- 
tors of Mill's view of Causation that we have con- 
sidered are, first, that causes are invariable ante- 
cedents of the facts or events we call effects, and 



CAUSATION 45? 

second, that causes are always complex groups of 
fact, the sum total of conditions, as Mill says, 
requisite to bring the effect into existence. There 
is still a third factor to which we may now give 
attention, a factor, it would seem, that occupies, in 
Mill's total view, a place which gives it a peculiarly 
special prominence. For, according to Mill, you 
may have a sequence displaying the features of com- 
plexity and invariability and not have one that is 
definitely causal. That is to say, B may have fol- 
lowed A invariably in our experience, and yet the 
ground or cause of the sequence A-B may really 
not be in A at all. The illustration, borrowed from 
Reid, that Mill uses is the sequence of night and 
day, in neither of which can the cause of the other 
be found, although there is no doubt that the em- 
pirical connection extends throughout human expe- 
rience. Some other factor, therefore, is required 
to complete the idea of cause, for, as Mill says, "it 
is necessary to our using the word cause that we 
should believe not only that the antecedent always 
has been followed by the consequent, but that as 
long as the present constitution of things endures 
it always will be so." Unless the sequence can also 
be regarded as 'unconditional/ we are not war- 
ranted, by Mill's view, in considering it to be caus- 
ally determined. "This is what writers mean when 
they say that the notion of cause involves the idea 
of necessity. . . . That which is necessary, that 
which must be, means that which will be, whatever 
supposition we may make in regard to all other 



458 A TEXT-BOOK OF LOGIC 

things. . . . That which will be followed by a 
given consequence when, and only when, some third 
circumstance also exists, is not the cause, even 
though no case should ever have occurred in which 
the phenomenon took place without it. Invariable 
sequence, therefore, is not synonymous with caus- 
ation, unless the sequence besides being invariable, 
is unconditional." 

It will be seen, at once, that in this statement, 
and only here, do we come, in Mill's view, face to 
face with the question, crucial for our comprehen- 
sion of causal relations, of what we must mean 
when we say that one event is necessarily connected 
with another. Now it should be remarked that this 
statement of Mill's raises questions which for their 
adequate discussion would require us to go outside 
the limits of inductive logic into the field of general 
metaphysics ; and this is true, not only for a student 
of the theory Mill proposes, but it is admitted as 
necessarily so by Mill himself. For, as he says, it is 
only so long as we can believe that the "present 
constitution of things endures," only so long, that 
is, as "the ultimate laws of nature (whatever they 
may be) as distinguished from the derivative laws 
and the collocations" remain unchanged, that what 
happens in experience can become a clue to what 
is true outside experience. In other words, it is 
only so long as the nature of reality is and remains 
what it is that we can argue from what has been 
to what will be in human experience. But the 
determination of the nature of reality, and of the 



CAUSATION 459 

relation that we as thinking and active individuals 
sustain toward it, is the definite problem of meta- 
physics, and only indirectly does this problem come 
into view in the discussion of logical questions. But 
even incidentally it is worth while to remark that 
the relation of logic to metaphysics that the position 
of Mill raises is such that, unless we can presuppose 
an ordered system of reality of some sort, our con- 
fidence in human knowledge is ultimately shaken, 
and the distinction between truth and error to a 
large extent is obliterated. For, as we have seen 
throughout, the nerve of human knowledge is to be 
found in the confidence we have that in all science 
and philosophy, and, we should say, in all art and 
religion as well, we are interpreting, not the empty 
shadows of a merely temporal experience, but the 
real nature of the world which is not only the sub- 
stance of all our knowing, but the very centre and 
core of the being which we as individuals possess. 

Turning, now, from these rather abstruce con- 
siderations, we must try to interpret Mill's position 
with respect to its logical implications. In order 
that we may understand exactly what Mill had in 
mind to say, it will be necessary to gain and secure 
a correct notion of the term in which he translates 
the necessity that belongs, as he and Hume before 
him admit, to our notion of cause. According to Mill, 
the necessity that we ascribe to a causal sequence 
has its foundation in the unconditional character 
of the causal sequence. What, then, does Mill mean 
by unconditional? The meaning that Mill attaches, 



460 A TEXT-BOOK OF LOGIC 

in a general way, to this word is perhaps not diffi- 
cult to detect, although he does not state definitely 
the sense in which it is understood. Most of his 
statements about it are negative. He says, for in- 
stance, that "that which will be followed by a given 
consequent when, and only when, some third cir- 
cumstance exists, is not the cause," the meaning 
evidently being that it is a cause only when the 
consequent follows without such mediation. And, 
again, he says that "if we adopt the convenient 
modification of the meaning of the word cause which 
confines it to the assemblage of positive conditions 
without the negative, then instead of "uncondition- 
ally," we must say, "subject to no other than neg- 
ative conditions," where, again, the absence of some 
third circumstance is necessary for determining an 
unconditional sequence. The point that Mill seems 
to make is that a sequence is unconditional when the 
consequent is seen to follow from the totality of 
conditions which constitute its cause, without any 
aid from any other circumstance which falls outside 
its cause as thus determined. 

Two remarks may help to make the meaning of 
this statement clearer. In the first place, Mill's 
view leaves out of account, as indeed it has a right 
to, such metaphysical considerations as were re- 
ferred to a little while ago. However impossible 
such a procedure would be if Mill were discussing 
the causal problem from the standpoint of the phil- 
osophy of knowledge, it is quite possible and even 
necessary when he is concerned merely with the 



CAUSATION 461 

invariable connections that are built up in the course 
of human experience. The denial, therefore, that 
any "third circumstance" operates in an uncondi- 
tional sequence cannot be meant, by Mill, to refer 
to the "constitution of things" which, as we saw, 
is in some sort the foundation on which all human 
knowledge in the long run depends. In the second 
place, we may remark that the "third circumstance," 
on the absence of which from any sequence the 
unconditionality of the cause is determined, must be 
interpreted to mean some third phenomenal circum- 
stance, some further fact or event of human expe- 
rience the same in kind as those that enter into the 
causal relation. What this statement amounts to 
is the declaration that whenever any causal se- 
quence has been determined, it will be found to 
include all those positive factors on which the occur- 
rence of the phenomenon depends, and that it is 
only when all such factors are present that the 
sequence is necessary, or, in Mill's term, uncondi- 
tional. It may help to bring out the significance of 
such a statement if we say that when the stated 
conditions are satisfied in any given case, we can 
argue not only from the occurrence of the cause to 
the occurrence of the effect, but also from the occur- 
rence of the effect to the occurrence of the cause. 
The presence of either the cause or effect necssarily 
implies the presence also of the effect or the cause. 
The Plurality of Causes. In view of the fact that 
the aim of science is to point out a connection be- 
tween a particular event and the totality of condi- 



462 A TEXT-BOOK OF LOGIC 

tions on the presence of which the event takes place, 
and on the absence of which it does not take place, 
we may ask how this conception of the aim of 
science is affected by the fact that the same event 
may occur for very different reasons. Now about 
such a fact there is no qusetion. It was fully recog- 
nised, for instance, by Mill who tersely remarks 
that "it is not true that the same phenomenon is 
always produced by the same cause." The fact, 
then, is that an event M may be caused now by A, 
and, again, by B or C or D. This fact is known, in 
the terminology of Mill, as the plurality of causes. 
What effect, we may ask, does the recognition of 
such a plurality of causes have upon our view of 
the nature of causation as expounded in the pre- 
ceding paragraphs? 

If we consider this question strictly from the 
point of view of what we have seen the relations 
between cause and effect in a causal sequence must 
be, it is obvious that we can not regard those events 
whose occurrence depends on a possible plurality of 
antecedents as causally related events at all. It 
was said just now that in a causal sequence we must 
be able, not only to argue from the occurrence of 
the antecedent to that of the consequent, but also 
to argue from the occurrence of the consequent to 
that of the antecedent. Now the significance of 
such a connection between antecedent and conse- 
quent in a causal sequence is that it goes far beyond 
what, in an earlier chapter, we saw was formally 
possible when we were considering merely hypo- 



CAUSATION 463 

thetical statements of fact. The rule concerning 
hypothetical statements, 'If A then B' for example, 
made it clear that from the occurrence of B we 
could say nothing with respect to the occurrence 
of A, and the reason assigned was that B might 
have occurred for some other reason than A. In 
other words, we had to recognise the possibility of 
what Mill calls the plurality of causes. Now the 
necessity for such a rule for dealing with the facts 
of our general experience is quite obvious when we 
consider that, with the development of science, there 
has come to be recognised a marked difference be- 
tween empirically connected events and causally 
related events, and, consequently that until the 
causal character of a particular sequence has been 
established, we cannot be certain that one rather 
than another group of possible antecedent condi- 
tions, as a matter of fact, has been the occasion of 
any given consequent. 

We may also point out that the recognition of a 
plurality of causes, if we emphasise the word cause 
in Mill's phrase, would necessarily throw our whole 
conception of cause into confusion, and there would 
remain for us no means of distinguishing between 
those events which were really connected as cause 
and effect, and those whose connections depended, 
in Mill's words, on some "third circumstance," 
events, that is to say, which are connected merely 
after the manner of an empirical juxtaposition. 
The distinction between causal sequences and em- 
pirical ones is important, it marks one of the gains 



464 A TEXT-BOOK OF LOGIC 

that have been acquired as the result of much 
labour, and it serves the distinctive purpose of map- 
ping out the fields with respect to which we may 
claim to have different degrees of knowledge. It 
is certainly true, for instance, that the inferences 
drawn from our ordinary experience are enter- 
tained much less confidently than are those that 
rest on the foundation of a scientific induction. In 
the latter case alone do we have certainty; in the 
former, we reach only a higher or lower degree of 
probability. And the difference between certainty 
and probability rests, in part at least, on the fact 
that in the case of certain knowledge all the factors 
material to it are known, and in the case of prob- 
ability we have no reason for believing that this 
requirement has been satisfied. And this statement 
enables us to see why it is that analysis plays so 
large a part in the method not only of the sciences 
but of philosophy as well, and why it is that, from 
the times of the Greeks, the distinction, based on the 
application of a method of analysis to the facts of 
experience, between opinion and knowledge, be- 
tween the popular beliefs of an age on the one hand, 
and carefully established truths on the other, has 
been regarded as a condition of intellectual culture 
and progress. We cannot, therefore, entertain any 
suggestion of treating the two classes of connection, 
the causal and the empirical, as if no distinction had 
been made between them, and we cannot do so be- 
cause all scientific advancement depends on it, and 



CAUSATION 465 

because it would leave us without any adequate 
conception of what we should mean by a cause. 

The result of our consideration of the conception 
of a plurality of causes amounts to this, that when 
we look at the conception from the standpoint of a 
carefully stated view of what causation implies, it 
seems to be a quite misleading, if not mischievous, 
conception. But, it may be objected, this result can 
be reached and maintained only if we allow a some- 
what strict interpretation of the causal relation to 
determine the view we take as to the possibility of a 
plurality of causes. That is exactly true. But the 
recognition of its truth does not require us to alter 
our notion of the causal relation, but to indicate the 
field within which the operation of more than a 
single set of antecedents as a condition of the occur- 
rence of a given fact or event may be said to occur. 
What we have seen is that the field of causally estab- 
lished relations is not such a field. For science in the 
strict sense of that term there is only one group of 
conditions that can be inferred from the occurrence 
of any given event. But when we remark that, as 
compared with the broad extent of our ordinary 
experience, the causal field is only a very small 
area, we see at once that, when we go outside this 
field, there must be possible some other than a 
causal interpretation of the sequences that occur. 
It follows, therefore, that we must go outside the 
field of the natural sciences if, looking at our expe- 
riences from the standpoint of their temporal rela- 
30 



466 A TEXT-BOOK OF LOGIC 

tions, we wish to emphasise and illustrate the possi- 
bility and nature of a plurality of causes. Nowhere, 
except in the sciences, can we argue from conse- 
quent to antecedent. The relations of antecedent 
and consequent, therefore, that occur in our ordi- 
nary experience, are not, in the strict sense, causal 
relations at all. And because they are not, it seems 
altogether misleading to speak of these relations as 
involving a plurality of causes. What a discussion 
of the possibility of a plurality of causes forces on 
us is, then, the recognition of a type of experience 
which implies no more than a plurality of ante- 
cedent or concurrent conditions. To call these con- 
ditions, in their relation to the event with which 
they are connected in our experience, causal is to 
go beyond what we know about them; for, as we 
have said, the test of a causal relation is that we 
can argue, not only from a given set of conditions 
to the conditioned, but also from the conditioned 
to a particular set of conditions. It is exactly the 
impossibility of doing this latter that led Mill, in 
the class of cases we are now considering, to speak 
of a pluarlity of causes, and which leads us to speak 
of a plurality of conditions. If, by our terminology, 
we can keep clearly before ourselves the fact that 
the relations which we are now considering are not 
causal, in the strict sense of that word, but that they 
are connected empirically merely in our experience, 
it will be passible to set over against each other the 
two types of experience, and to entertain the prob- 
lem, which the non-causal relations certainly sug- 



CAUSATION 467 

gest, whether these latter can all be reduced to a 
single causal type. Although it takes us outside the 
limits of our present inquiry, we may hazard the 
remark that perhaps human life and experience are 
too rich and complex to be capable of interpretation 
throughout in terms of any single class of relations. 

REFERENCES 

H. A. Aikins, The Problem of Logic, Chs. XXVI., XXVIL, 
XXVIII., XXIX. 

J. E. Creighton, An Introductory Logic, 3d Edition, Chs. 
XVI., XVII. 

J. G. Hibben, Logic, Deductive and Inductive, Chs. IV., V., 
VI., VII., VIII., IX., X. 

W. S. Jevons, Elementary Lessons in Logic, Lessons XXVIII., 
XXIX. 

S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
tion, Ch. IX. 

W. Minto, Logic, Inductive and Deductive, Chs. III., IV., V., 
VI., VII. 

C. Read, Logic, Deductive and Inductive, 3d Edition, Chs. 
XIV., XVI. 

W. J. Taylor, Elementary Logic, Ch. XVII. 

ADVANCED 

B. Bosanquet, Logic, Vol. I., Book I., Ch. VII. 

F. H. Bradley, The Principles of Logic, Book. II., Part II., 

Ch. III., Book III., Part II., Ch. II. 
W. R. B. Gibson, The Problem of Logic, Chs. XLIL, XLIV., 

XLV., XLVI. 
H. W. B. Joseph, An Introduction of Logic, Chs. XIX., XX., 

XXII. 
J. S. Mill, A System of Logic, Book III., Chs. V., VI., VIII., 

IX., X., V. 



468 A TEXT-BOOK OF LOGIC 

F. C. S. Schiller, Formal Logic, Chs. XX., XXI. 
J. Venn, Empirical Logic, Ch. XVII. 

J. Welton, A Manual of Logic, Vol. II., Book V., Chs. I., 
§§ 143, 144, V., § 155. 

QUESTIONS 

1. In what general fact of observation does the problem of 
causation originate? 

2. How, in view of this fact, may the causal problem be 
stated? 

3. Explain what is meant by saying that the causal prob- 
lem is practical before it is theoretical. Illustrate. 

4. In what way does the practical aspect of the problem of 
causation tend to develop human intelligence? 

5. Describe as accurately as you can the precise nature of 
the regularities in experience which we are led to ob- 
serve from the practical point of view. 

6. In what two respects does the theoretical differ from the 
practical view of causation, and what advantages are 
thereby secured? 

7. State and illustrate Mill's criticism of the practical and 
theoretical conceptions of cause. 

8. Show, by means of illustrations, that the practical and 
theoretical conceptions of cause are genetically related. 

9. In what way has the theoretical notion of cause reacted 
upon the practical to give it a more definite and extended 
meaning? 

10. What is meant by saying that the causal problem arises 
from the importance of order in human experience? 

11. 'The causal problem is concerned with the question of 
how things happen as they do.' Explain. 

12. What, according to Mill, is the first characteristic of a 
causal relation? 

13. What is meant by the time relations of causal events? 

14. How far do you agree with Mill that the cause of an 
event is its invariable antecedent? 



CAUSATION 469 

15. What can you say with respect to the view that there 
is no essential difference between a cause and an effect. 

16. Explain what is meant by the temporal continuity of 
causal events. 

17. What, according to Mill, is the second characteristic of 
causal relations, and to what two facts of importance 
does it direct attention? 

18. What does Jevons mean by the occasion of an event as 
contrasted with its cause? What other term is some- 
times used for Jevons' 'occasion'? 

19. Give three reasons for emphasising the complex charac- 
ter of causes. 

20. What can be said for and against selecting one of the 
conditions of an event and calling that the cause? 

21. In what way would your answer to the previous ques- 
tion be affected by the consideration that one's interest 
in the causal relation is practical and not theoretical? 

22. What, according to Mill, is the third characteristic of 
causal relations? 

23. Does Mill recognise the 'necessity' of causal relations, 
and, if so, what does he mean by necessity? 

24. Does Mill's view of causation imply an appeal to meta- 
physics, and, if so, in what respect? 

25. Explain what Mill means by unconditional. 

26. Is it possible, on Mill's view of causation, to argue from 
the occurrence of an effect to that of the cause? 

27. What is meant by the plurality of causes? 

28. If in any particular instance we admit a possible plu- 
rality of causes, how does that admission affect our con- 
ception of its strictly causal character? 

29. What is the difference between causally and hypothet- 
ically connected series of events? 

80. Why would it be preferable to speak of a plurality of 
conditions instead of a plurality of causes? 



470 A TEXT-BOOK OF LOGIC 



EXERCISES 

1. Enumerate six instances of regularity in the order of 
particular events which are of importance for the prac- 
tical life. 

2. Develop, from the theoretical point of view, the in- 
stances mentioned in your answer to the previous ques- 
tion in order to show to what question of scientific in- 
terest each may lead. 

3. Examine six instances of scientific causation for the 
purpose of showing how each satisfies the three condi- 
tions of a cause mentioned in the text. 

4. Examine the following and show in what respects they 
are, and in what respects they are not, statements of 
strictly causal relations. 

(1) In myexperience A has been invariably preceded 
by B, and we may therefore conclude that B is 
the cause of A. 

(2) Scarlet poppies, scarlet verbenas, the scarlet haw- 
thorne and honeysuckle are all odourless, there- 
fore we may conclude that all scarlet flowers are 
destitute of odour. 

6. Mention six instances which illustrate, what Mill calls, 
a plurality of causes. State for each instance the pos- 
sible causes. 



CHAPTER XVII 
MILL'S experimental methods 

Their Historical Position. The publication of 
Mill's System of Logic in 1843 gave, no doubt, a 
great impetus to the study of what is commonly 
known as inductive logic, and especially to the con- 
sideration of the principles that underlie the meth- 
ods by which, in the several sciences, causal relations 
are determined. Prior to Mill, however, interest in 
the inductive inquiry had had a somewhat long his- 
tory, and the reader will find in Minto's Logic (pp. 
243-272) an account of the course that this interest 
took from the time of the Franciscan monk, Roger 
Bacon (1214-1292), to the modern era which was 
ushered in, and whose development was determined 
by the progress of experimental science. That the 
advancement of learning, of which Francis Bacon 
(1561-1626) may be taken as the modern herald, 
should have maintained itself successfully for over 
two centuries, and that during that period natural 
science should have extended its scope as well as 
secured its position, could not be without its in- 
fluence upon the conception that was held of the 
nature and value of logical inquiries. In the pres- 
ence of such a solid body of achievement as came 
rapidly to the credit of the natural sciences, it was 
inevitable that interest should be aroused in the 
methods by which such results were gained. Con- 

(471) 



472 A TEXT-BOOK OF LOGIC 

sequently, we find that men of learning in this 
period gave considerable attention to the study of 
scientific methods, and in the first half of the nine- 
teenth century Herschel's discourse On the Study 
of Natural Philosophy, (1831), and WhewelPs two 
large volumes on the History of the Inductive Sci- 
ences, (1837), and his Philosophy of the Inductive 
Sciences, (1840), stand out prominently as contri- 
butions of capital importance to our understanding 
of the inductive procedure. Based as they are upon 
the facts of experimental science, and containing a 
description and analysis of the methods by which 
conclusions had been reached in the sciences, they 
constitute a repository of great value for any one 
who would study the theory of inductive science. 
With these books before him, Mill set out in his 
Logic, as he says, to "generalise the modes of inves- 
tigating truth and estimating evidence, by which so 
many important and recondite laws of nature have, 
in the various sciences, been aggregated to the 
stock of human knowledge." In the chapter on The 
Four Methods of Experimental Inquiry/ Mill gives 
an account of the various ways in which causal 
relations are or may be determined. In what fol- 
lows, we propose to describe these methods briefly, 
and shall limit ourselves chiefly to the task of stating 
and illustrating them. To determine the view that 
Mill took of them as a whole, or to estimate their 
value in detail, falls outside the scope of an elemen- 
tary study of logical problems. 



MILL'S experimental methods 473 

The Nature of the Problem to which these Methods 
Apply. In the foregoing chapter, we have seen that 
the causal relation, strictly interpreted, is reciprocal, 
that is, it is a relation between phenomena of such 
a kind that from the presence or absence of either 
term of the relation we can argue to the presence 
or absence of the other. The rise and fall of the 
mercury in a thermometer, for example, are recip- 
rocally related to the varying degrees of tempera- 
ture. To the establishment of such relations the 
sciences doubtless aspire in their investigation of 
the processes of nature. And that a considerable 
degree of success in this particular has been achieved 
in those sciences, such as physics and astronomy, 
which rest upon a mathematical foundation is suffi- 
cient to suggest, to those who are interested in the 
logic of the sciences, an inquiry to which the meth- 
ods of Mill are the direct answer. Mill's methods, in 
other words, are a statement of the processes which 
have been found useful in the establishment of those 
causal relations in which the antecedent and conse- 
quent reciprocally imply each other. But since recip- 
rocal relations have not been established between 
the antecedent and the consequent of all known 
phenomena, we should be putting an unnecessary 
strain upon these methods if we did not regard them 
as applying, in the strict sense, only to those special 
cases in which a relation of the kind in question 
had been determined. We may also remark that 
these methods are not offered by Mill as a substitute 
for the specialised modes of investigation which are 



474 A TEXT-BOOK OF LOGIC 

developed by each special science according to its 
needs. Indeed, the methods are quite general in 
nature, and could not have been formulated had not 
relations of the kind they imply been already suc- 
cessfully established. They must be understood, 
therefore, as revealing the logic of causal inquiries, 
when these inquiries have led to the determination 
of reciprocal relations between causes and effects. 

Elimination as a Method of Causal Inquiry. We 
have just seen that Mill's methods aim to state the 
general modes of procedure in those instances in 
which reciprocal causal relations have been estab- 
lished. In the light of this statement, it might seem 
superfluous to ask whether the causal inquiry rests 
upon the process of eliminating from the cause, or 
effect, those data whose presence or absence from a 
phenomenon makes no difference either to its occur- 
rence or non-occurrence. This is, indeed, the posi- 
tion that we should be inclined to adopt were it not 
for the fact that a difference of opinion exists as to 
whether, and in what sense, the methods, as Mill 
expounds them, depend upon such process of 
elimination. 

Joseph, for example, takes the view that "the 
causal circumstances are indicated by a process of 
exhaustive elimination." His position, more fully 
stated, is that, in view of the nature of causal rela- 
tions, certain particular requirements must be satis- 
fied by any instance which claims to involve a causal 
relation, and that the failure to satisfy any one of 
these requirements disproves that relation between 
two given phenomena. These requirements he enu- 



mill's experimental methods 475 

merates as grounds of elimination, and are as fol- 
lows: 

1. Nothing is the cause of a phenomenon in the 
absence of which it nevertheless occurs. 

2. Nothing is the cause of a phenomenon in the 
presence of which it nevertheless fails to occur. 

3. Nothing is the cause of a phenomenon which 
varies when it is constant, or is constant when it 
varies, or varies in no proportionate manner with it. 

4. Nothing is the cause of a phenomenon which 
is known to be the cause of a different phenomenon. 

These grounds of elimination are said by Joseph 
to be the foundations of Mill's inductive methods. 
The first is the foundation of the Method of Agree- 
ment; the second, of the Method of Difference; the 
first and second combined, of the Joint Method of 
Agreement and difference; the third, of the Method 
of Concomitant Variations; and the fourth, of the 
Method of Residues. It thus comes about, according 
to Joseph, that "Mill has not formulated four (or 
five) but one "Method of Experimental Inquiry" 
... of which the essence is that you establish 
a particular hypothesis about the cause of a phe- 
nomenon by showing that, consitently with the 
nature of the relation of cause and effect, the facts 
do not permit you to regard it as the effect of any- 
thing else (and mutatis mutandis if you are inquir- 
ing into the effect of anything)." Thus if I know 
that S must be caused by L or M or P or Q, because 
these are the instances in which the phenomenon 
occurs, then by testing each instance by the canons 



476 A TEXT-BOOK OF LOGIC 

of elimination I am able to discover the one rela- 
tion in which S stands that is reciprocally causal. 

Against this position Gibson argues that there 
is in Joseph's account a confusion between physical 
and logical elimination, and that when Mill speaks 
of the Methods of Agreement and Difference as 
methods of elimination he must be understood to 
mean the former and not the latter kind of elimina- 
tion. The meaning of this contention is quite clear 
if by physical elimination is understood the method 
of excluding from a phenomenon certain elements 
which are found not to have an effect upon the occur- 
rence or non-occurrence of the phenomenon. By 
logical elimination, on the other hand, is meant the 
rejection of certain hypotheses — as, for example, 
some of the alternatives in a disjunctive proposi- 
tion — with respect to the causal connection. In 
this case, we are rejecting the non-causes as a 
means of discovering the true causes. There is a 
certain presumption in favour of Gibson's conten- 
tion, for Mill himself says that elimination is a term 
"well suited to express the operation . . . which 
has been understood since the time of Bacon to be 
the foundation of experimental inquiry — namely, 
the successive exclusion of the various circumstances 
which are found to accompany a phenomenon in a 
given instance, in order to ascertain what are those 
among them which can be absent consistently with 
the existence of the phenomenon." But whether 
any or all of Mill's Methods are based upon a single 
type of elimination can be decided only by exam- 



MILL'S experimental methods 477 

ining the methods themselves. For the present, it is 
enough to have stated the nature of the difference 
between the views that are held of the relation of 
elimination to the Methods that we are about to 
study. 

The Method of Agreement. Mill states the prin- 
ciple upon which this Method rests as follows: 
If two or more instances of the phenomenon under 
investigation have only one circumstance in common, 
the circumstance in which alone all the instances agree 
is the cause (or effect) of the given phenomenon. 
The requirement that the instances in question 
shall have only one circumstance in common can not 
be satisfied unless all the other circumstances that 
are relevant to the phenomenon are different. Not 
any enumeration of instances, therefore, would sat- 
isfy the conditions of this Method, but only one in 
which all the instances, however much they may 
differ from one another, are alike in only a single 
particular. When, then, two or more instances of a 
phenomenon are shown to have only one circum- 
stance in common, that circumstance, according to 
Mill, is the cause or the effect of the phenomenon. For 
this reason, the Method has been called the Method 
of Single Agreement, and is formulated by Jevons 
as follows : The sole invariable antecedent of a phe- 
nomenon is probably its cause. An illustration bor- 
rowed from Bain, may be given. "The North-East 
wind," Bain writes, "is generally detested in this 
country ; as long as it blows, few people are at their 
best. Occasional well known causes of a wind being 



478 A TEXT-BOOK OF LOGIC 

injurious are violence, excessive heat or cold, ex- 
cessive dryness or moisture, electrical condition, the 
being laden with dust or exhalations. Let the hypo- 
thesis be that the last is the cause of the North- 
East wind's unwholesome quality; since we know 
it is a ground current setting from the pole toward 
the equator and bent westward by the rotation of 
the earth; so that, reaching us over thousands of 
miles of land, it may well be fraught with dust, 
effluvia, and microbes. Now, examining many 
cases of North-East wind, we find that this is the 
only circumstance in which all the instances agree; 
for it is sometimes cold, sometimes hot; generally 
dry ; but sometimes wet ; sometimes light, sometimes 
violent; and of all electrical conditions. Each of 
the other circumstances, then, can be omitted with- 
out the North-East wind ceasing to be noxious ; but 
one circumstance is never absent — namely, that it 
is a ground current. That circumstance, therefore, 
is probably the cause of its injuriousness. ,, 

It will be observed from this illustration that the 
Method is essentially a method of elimination; its 
use depends upon the possibility of analysing the 
phenomenon into its constituent parts, and of select- 
ing from among them the one that is causal. It is 
evident, therefore, that the method cannot begin to 
be put into operation until we have before us at 
least two instances of the phenomenon, and that 
the reliability of the Method is much increased with 
an increase in the number and variety of the in- 
staces that are examined. In view of such facts 



MILL'S EXPERIMENTAL METHODS 479 

as these, Mellone has formulated the method as 
follows: When observation shows that two events 
accompany one another (either simultaneously or in 
succession), it is probable that they are causally con- 
nected ; and the probability increases with the number 
and variety of the instances. 

When this Method speaks of causes as single 
antecedents, it is evident that it presupposes that 
the phenomenon under investigation has been sub- 
jected to analysis, and that in this way its elements 
have been distinguished. Now, with respect to the 
supposition that causes are to be discovered among 
the elements into which the phenomenon is anal- 
ysed, there are two question to be asked. The first 
is, are we certain, in view of the inter-connection 
of all parts of the known universe, that single events 
ever do act in isolation from all the rest? But not 
to press the point in that form, are we certain that 
within particular universes, that is, with reference 
to particular groups of events, we can analyse a 
point for point concomitance between causes and 
effects? For instance, is the "ground current" of 
the illustration used above, on any supposition, a 
single antecedent? Is it not merely another name 
for "dust, effluvia, and microbes"? If, however, it 
be replied that the object of science is to establish 
causal connections between single antecedents and 
consequents, we may ask, in the second place, 
whether there exists any means of assuring our- 
selves that the analysis of a particular phenomenon, 
however complete it may seem, has succeeded in 



480 A TEXT-BOOK OF LOGIC 

detecting all of the factors present in the event that 
we call its cause? For a long time, for example, 
air was regarded as an element; and even since its 
analysis into oxygen, nitrogen, hydrogen, carbon 
dioxide, etc., modern chemistry has discovered still 
other elements in certain quantities. It may very 
well happen, therefore, that any supposed single 
antecedent is really complex. In most cases, it is 
only a relative simplicity that can be attained, a 
simplicity that is met with at the point where our 
methods of analysis are unable to carry us any 
further. We conclude, therefore, that the Method 
states an ideal that, in practice, is difficult to attain, 
and, when attained, to definitely certify. 

What degree of confidence, we may ask, may be 
reposed in the results that are attained by the use 
of this Method? In other words, what are the limits 
of its usefulness? To be more specific still, is it 
distinctively a method by which we are able to ex- 
plain the occurrence of phenomena? This question 
we must answer in the negative. The Method of 
Agreement is, as one has said, "a mode of recon- 
noitering," a method for delimiting the area within 
which causal relations may, with some degree of 
confidence, be expected to exist. But for the estab- 
lishment of such relations we should have to pass 
beyond the method itself. Let us suppose, for 
example, that three instances of a phenomenon may 
be analysed in the following schematic way: 



mill's experimental methods 481 

[ABC ' x y z] 

Antecedents |A B'C xy'w I Consequents 

[A E F x v uj 

Are we certain, in such a case, that A, the circum- 
stance in which all the antecedents agree, is the 
cause of the phenomenon ? Starting with the obser- 
vation of x, does it follow, because our analysis of 
all the instances of x shows A to be the one element 
that is common to these instances, that A is, there- 
fore, the cause of x ? Mill has pointed out in answer 
to such questions that their affirmative answer 
would take us beyond the limits of this Method, 
when and so long as we are obliged to consider, in 
our interpretation of the instances, the possibility 
of a plurality of causes, the possibility, that is, that 
x may be produced by more than one cause. If the 
instances of the phenomenon were known to be 
reciprocal, or if we were certain that we had all 
the instances before us, the situation would be 
different; but so long as neither condition is guar- 
anteed, it only remains probable, as Jevons' and 
Mellone's formulations of the Method indicate, that 
the "one circumstance in common" is the cause of 
the phenomenon in question. It thus appears, to 
quote Mill, that the Method of Agreement "leads 
only ... to unifomities, which either are not laws 
of causation, or in which the question of causation 
must for the present remain undecided. The Method 
of Agreement is chiefly to be resorted to as a means 
of suggesting applications of the Method of Differ- 

31 



482 A TEXT-BOOK OF LOGIC 

ence, ... or as an inferior resource in case the 
Method of Difference is impracticable; which . . . 
generally arises from the impossibility of artificially 
producing the phenomena, ,, that is, when experi- 
mentation is not possible. 

The Method of Difference. The Method of Agree- 
ment, as we saw, is a method of systematic obser- 
vation, and its object, negatively stated, is to elim- 
inate from the occurrences of a particular phenom- 
enon those elements which, because they are not 
constant in all the instances, cannot be regarded as 
being the cause, or part of the cause of the phenom- 
enon, and thus, affirmatively stated, to map out the 
area within which the cause may probably be found. 
Turning now to the Method of Difference, we find 
that it is a method of scientific experiment, and 
the formulation given it by Mill is as follows: If 
an instance in which the phenomenon under inves- 
tigation occurs, and an instance in which it does not 
occur, have every circumstance in common save one, 
that one occurring only in the former, the circum- 
stance in which alone the two instances differ is the 
effect, or the cause, or an indispensable part of the 
cause, of the phenomenon. Let us suppose, for ex- 
ample, that two instances of a phenomenon can be 
analysed schematically as follows : 

[ABC xyzl 

Antecedents 1 y Consequents 

I B C yzl 



MILL'S EXPERIMENTAL METHODS 483 

then we may say, according to this Method, that A 
is the cause of x. Thus, let us suppose that in two 
glasses equal quantities of lemon juice and water 
are mixed, and that in one of them a given quantity 
of sugar is dissolved. The taste of the liquid which 
contains the sugar, we shall say, is pleasant, and 
the taste of the liquid which does not contain sugar 
is unpleasant. What is the cause of the pleasant 
taste? The circumstance, says Mill, in which alone 
the two instances differ, namely, the sugar. 

In calling the Method of Difference a method of 
scientific experiment, we may observe that scientific 
experimentation, as this was defined above, involves 
a definite control of the conditions under which a 
phenomenon occurs, and a definite inquiry to which 
the experiment is expected to give an affirmative or 
negative answer. Scientific experiment is like a 
shafted arrow, it is aimed at a mark, and its course 
toward that mark is controlled, as is the arrow 
which is sped from the bow. To illustrate, let us 
suppose that we wished to know why a feather, 
dropped simultaneously from the same height as a 
coin, reaches the ground after the coin. Our ques- 
tion will be, Is the greater resistance offered by the 
air to the feather the cause of the observed phe- 
nomenon? To answer this question, we must insti- 
tute an experiment, and to do this, as we said, it is 
necessary to bring the phenomenon under controlled 
conditions. Thus, we first drop the two objects 
from the same level and at the same time in, let us 
say, the receiver of an air-pump. The feather is 



484 A TEXT-BOOK OF LOGIC 

observed to flutter to the base of the pump after 
the coin. We perform the same experiment again, 
with the exception that we take care to remove all 
the air from the receiver. Under these conditions, 
the coin and the feather reach the base of the re- 
ceiver at the same time. The conclusion is that the 
only circumstance in which the two instances differ, 
namely, the presence of air in the former, is the 
cause of the phenomenon. Because, as in this ex- 
ample, the Method proceeds systematically by 
changing one condition at a time, it is known as 
the Method of Single Difference, and the following 
formulation has been given by Mellone: When 
the addition of an agent is followed by the ap- 
pearance, or its subtraction by the disappearance, of 
a certain event, other circumstances remaining the 
same, that agent is causally connected with the event. 
Or, to state the principle on which any formulation 
of the Method relies, we may say that the circum- 
stance in the absence of which a phenomenon fails to 
occur is the cause, or part of the cause, of the phe- 
nomenon. 

It will add to the clearness of our apprehension 
of the meaning of this Method, if we distinguish 
the instances of the phenomenon that are success- 
ively observed. For this purpose, let us call the 
instance in which the suspected cause occurs the 
positive instance, and the one in which it does not 
occur the negative instance. By this terminology 
is meant that, in what is called the positive in- 
stance, we have the occurrence of the observed phe- 



mill's experimental methods 485 

nomenon along with the occurrence of its supposed 
cause, and, in the negative instance, the absence of 
the phenomenon together with the absence of the 
supposed cause. 

In view of this distinction, it will be seen that 
the Method depends, for its validity, on the negative 
instances through which a suspected cause is either 
proved or disproved. And, for this reason, it rightly 
insists on the importance of varying only one condi- 
tion of the phenomenon at a time. For if we were to 
vary simultaneously two of a phenomenon's condi- 
tions, and found that some change resulted, we 
should be unable to tell whether this change was due 
to one of the altered conditions, or to the other, or 
to the joint action of both. And if no change en- 
sued, we could not safely conclude that neither con- 
dition was affective, for the action of the one may 
have been neutralised by that of the other. And 
even when only a single condition is varied at any 
one time, it is important, as Mill pointed out, that 
the experiment should be conducted with dispatch, 
and its entire process brought as rapidly as possible 
to an end. The reason for this caution is that if the 
experiment is to serve the purpose for which it was 
instituted, the effect must be the effect solely of the 
one altered condition. If, on the contrary, during 
the course of an unusually prolonged experiment, 
the original conditions of the experiment were mod- 
ified by the development of changes which deter- 
mined in part the character of the observed effect we 
should have, what Mill called, an inter-mixture of 



486 A TEXT-BOOK OF LOGIC 

effects ; and this would be as destructive of the value 
of the Method as any unsystematic variation in the 
conditions themselves. 

It is a well known fact that not all problems are 
capable of experimental handling, and that those 
that are, are liable to have their results affected by 
the operation of conditions which we can in no 
wise eliminate. In the former case, the Method of 
Difference cannot be used. In the latter, the condi- 
tions referred to are those that belong to the struc- 
ture of the universe to which the particular phenom- 
enon belongs. Such conditions Mill called perma- 
nent causes. "The pendulum, for example, has its 
oscillations disturbed by the vicinity of a mountain." 
What, in such a case, can be done to make the 
Method applicable? It is evident that we cannot 
remove the mountain, but, as Mill points out, we 
can take the pendulum to a locality where the 
mountain's interference is reduced to a minimum. 
In this way, it ceases to be an "influencing agent," 
and becomes merely a "co-existing fact." When an 
experiment cannot be removed outside the sphere of 
the operation of such permanent causes, recourse 
may be had to the Method of Concomitant Variations 
which is discussed below. 

The Joint Method of Agreement and Difference. 
There is, no doubt, something ideal in the require- 
ments that are laid down as conditions of the use of 
the Methods of Agreement and of Difference. It is 
rarely that in the course of common life or scientific 
investigation a number of instances are given which 



mill's experimental methods 487 

agree or differ in only a single instance. There 
seems to be, therefore, a breach between experience, 
on the one hand, and these modes of establishing 
causal relations, on the other. Either, then, we 
shall have to say that the Methods of Agreement 
and of Difference are of only limited application, 
and that causal connections cannot be established 
in a great deal of our experience, or that, with re- 
spect to that part of experience which does not come 
directly within the scope of these Methods, some 
other means of determining causal connections must 
be used. It is to meet the latter of these alternatives 
that the Joint Method of Agreement and Difference 
is particularly useful. The formulation of this 
Method by Mill was made necessary in view of the 
fact, as he says, that there are "many cases in which, 
though our power of producing the phenomenon is 
complete, the Method of Difference either cannot be 
made available at all, or not without a previous em- 
ployment of the Method of Agreement. This occurs," 
says Mill, "when the agency by which we can pro- 
duce the phenomenon is not that of one single ante- 
cedent, but a combination of antecedents, which we 
have no power of separating from each other and ex- 
hibiting apart." Besides those cases in the natural 
sciences which Mill had in mind, the Joint Method 
will be found applicable, as Creighton has pointed 
out, when we try "to reach generalizations regard- 
ing the behaviour of human individuals or human 
societies — in looking for moral, or social or eco- 
nomic laws," 



488 



A TEXT-BOOK OF LOGIC 



The Joint Method is formulated by Mill as fol- 
lows: If two or more instances in which the phe- 
nomenon occurs have only one circumstance in com- 
mon, while two or more instances in which it does 
not occur have nothing in common save the absence 
of that circumstance, the circumstance in which alone 
the two sets of instances differ is the effect, or the 
cause, or an indispensable part of the cause, of the 
phenomenon. Thus, we are concerned, in this 
Method, with two sets of instances, one set of posi- 
tive instances, in which thei phenomenon with its 
suspected cause is present, and one of negative 
instances, in which the phenomenon with its sus- 
pected cause is absent. When these conditions are 
satisfied,, the Method affirms that the circumstances 
in which the two sets of instances differ is causally 
connected with the phenomenon. Let us suppose, 
for example, that two sets of instances, positive and 
negative, can be, schematically, analysed as follows : 



Antecedents 



POSITIVE INSTANCES 



A B C D 
A B E F 
A C F G 




Consequents 



Antecedents 



NEGATIVE INSTANCES 



B C D E 
C F G H 
E H J K 




Consequents 



A comparison of these instances shows that wfcm 
x is present A is present, and that when x is absent 



mill's experimental methods 489 

A is absent, and this suggests that A and x are 
causally connected. But we cannot prove this by 
the Method of Agreement, because there are no two 
instances which agree in having only a single cir- 
cumstance is common; and we cannot prove it by 
the Method of Difference, because there are no two 
instances which differ in no respect except in the 
presence of A and x in the positive instances, and 
their absence in the negative ones. Moreover, it 
will be observed that the instances supposed do not 
conform strictly to the requirements of Mill's state- 
ment, and that it is exactly this divergence that sets 
the problem which this Method is intended to solve. 
In other words, the agreements and differences are 
greater in the instances we have supposed than they 
have any right to be on a strict interpretation of 
Mill's statement. The reason for this divergence is 
that Mill's statement of the Method, as Mellone 
remarks, "is vague, and it is incorrect in more than 
one point; two positive instances would never be 
enough, still less could two negative instances ; and it 
is not necessary that the negative instances should 
have 'nothing in common'," and, as our illustration 
shows, it is not necessary that the positive instances 
should agree in only a single circumstance. With 
these amendments in view, we may quote Mellone's 
proposed formulation of the Method: Whatever is 
present in numerous observed instances of the pres- 
ence of the phenomenon, and absent in observed 
instances of its absence, is probably connected caus- 
ally with the phenomenon. 



490 A TEXT-BOOK OF LOGIC 

How, now, can we proceed to apply the Method? 
If we examine the positive instances, employing for 
that purpose the general principle of the Method 
of Agreement, we shall see that in the first two 
cases A or B or AB is the cause of the phenomenon 
x, since A and B are the only conditions present in 
both. For a similar reason, we see that A or C or 
AC is the probable cause of the phenomenon in the 
first and third cases; and that the cause in the 
second and third cases is probably A. Now if the 
probable cause in all these instances is the same, that 
cause must be A, since that is the only particular in 
which they all agree. If, now, we examine the neg- 
ative instances, employing for that purpose the gen- 
eral principle of the Method of Difference, we note 
that they all agree in the absence of A and x, and 
that this is the only relevant circumstance in which 
they do agree. The absence in the negative instances 
of the supposed cause of x along with the absence of 
x, when taken in connection with the relative 
unimportance of the other circumstances, greatly 
strengthens the supposition that was reached as the 
result of examining the positive instance, namely, 
that A is the cause of x. Such a Method as the one 
here outlined has been called by various names. Mill 
spoke of it sometimes as "a double employment of the 
Method of Agreement," whence it is often called the 
Method of Double Agreement. Mill also spoke of it 
as the Indirect Method of Difference. But the name 
by which it is commonly known is the Joint Method 



MILL'S EXPERIMENTAL METHODS 491 

of Agreement and Difference, a name which Mill 
also used in referring to the method. 

The following application of the Joint Method 
to a social problem illustrates so well, not only its 
usefulness in this class of problem, but the nature 
of the Method itself, that we shall quote it entire. 
"We may suppose," Creighton writes, "that in a 
certain part of the country it was noticed that a 
considerable difference existed in the number of 
criminal offenses committed, in proportion to the 
number of inhabitants, in the various towns. In 
several towns the percentage was high, while in 
others it was relatively small. This being so, a 
question naturally arose as to the cause of the high 
percentage. Now there were among the people 
various opinions concerning the matter. . . . Not 
being able to agree about the matter, it was decided 
to appoint a committee to investigate the circum- 
stances existing in various towns where the same 
general conditions prevailed, and upon the basis of 
this comparison to decide. The towns with a high 
criminal percentage were examined first. The re- 
port of conditions there was as follows : 

Town A: Small police force — efficient schools — severe pen- 
alties — inactive churches — licensed saloon. 

Town B: Small police force — efficient schools — light penal- 
ties — active churches — licensed saloons. 

Town C : Large police force — inefficient schools — severe pen- 
alties — active churches — licensed saloons. 

Town D: Large police force — inefficient schools — light pen- 
alties — inactive churches — licensed saloons. 



492 A TEXT-BOOK OF LOGIC 

"This report revealed the fact that in each of 
these towns having a high criminal percentage there 
was one circumstance, and only one, invariably 
present, — the licensed saloon. This rendered it 
probable that the saloon was the cause of the high 
percentage of crime. Still, before finally deciding, 
it was thought well to investigate negative instances 
as well ; that is, towns in which the high percentage 
of crime did not occur. The report of conditions 
there was as follows: 



Town E 
Town F 
Town G 
Town H 



Large police force — efficient schools — light penal- 
ties — active churches — no licensed saloons. 
Large police force — inefficient schools — light pen- 
alties — active churches — no licensed saloons. 
Small police force — efficient schools — light penal- 
ties — inactive churches — no licensed saloons. 
Small police force — inefficient schools — severe pen- 
alties — active churches — no licensed saloons. 



"This table showed that in the absence of the 
phenomenon (high criminal percentage) one and 
only one of the conditions concerned was invariably 
absent ; namely, the licensed saloon. This confirmed 
the previous report and established to the satisfac- 
tion of all that the saloon was, at least, the main 
cause of the high criminal percentage in the cities 
concerned." 

The Method of Concomitant Variations. Mill 
states this Method as follows : Whatever phenom- 
enon varies in any manner whenever another phe- 
nomenon varies in some particular manner, is either 



MILL'S EXPERIMENTAL METHODS 493 

a cause or an effect of that phenomenon, or is con- 
nected with it through some fact of causation. The 
Method presupposes two classes of cases. Whenever, 
for example, any variation in one phenomenon ac- 
companies a variation in another, these phenomena 
may either be related directly as cause and effect, 
or they may be "two different effects of a common 
cause.' ' The Method itself, however, does not enable 
us to decide, in any particular instance, which of 
these alternative possibilities is realised. In order 
to decide that point, as Mill says, we should have to 
determine whether one set of the variations in ques- 
tion were capable of being produced by means of the 
other. In that case, the relation is one of cause and 
effect. If, on the other hand, the variations in ques- 
tion were not capable of being produced in the man- 
ner indicated, we should have to regard them as 
effects of a cause that is common to both. In both 
cases the principle on which the Method rests is 
that "anything on whose modifications, modifica- 
tions of an effect are invariably consequent, must 
be the cause (or connected with the cause) of that 
effect," As an example, "let us suppose," to quote 
Gibson, "that an electric bell is placed ringing under 
the receiver of an air-pump. The air is now grad- 
ually exhausted, and it is noticed that, parri passu 
with the exhaustion of the air, the sound of the 
bell grows fainter and fainter, until a point is 
reached at which it is no longer heard at all. The 
air is now allowed to pass back gradually into the 
receiver, and, as it does so, the sound of the bell is 
heard, at first faintly, then more and more loudly, 



494 A TEXT-BOOK OF LOGIC 

until the clearness of the original note is repro- 
duced." 

The Method of Concomitant Variations, as Mill 
himself indicated, is applicable particularly to those 
cases in which the Method of Difference, on account 
of the impossibility of removing the phenomenon 
under observation from the influence of permanent 
causes, entirely fails. Let us suppose, to take one 
of Mill's illustrations, that we wished to know what 
influence the moon exerts on the surface of the 
earth. "We cannot try an experiment in the absence 
of the moon, so as to observe what terrestrial phe- 
nomena her annihilation would put an end to; but 
when we find that all the variations in the position 
of the moon are followed by corresponding varia- 
tions in the time and place of high water, the place 
being always either the part of the earth which is 
nearest to, or that which is most remote from, the 
moon, we have ample evidence that the moon is, 
wholly or partially, the cause which determines the 
tides." 

Sometimes it is not the mere concomitance 
of varying phenomena, but the varying quantities 
of the associated phenomena, that leads to the deter- 
mination of a causal relation between these phenom- 
ena. If, for example, a connection between heat and 
expansion is suspected, we can increase or diminish 
the amount of heat, and observe whether, under 
the varying conditions, any corresponding varia- 
tions occur in the expansions of a heated body. That 
increase of heat is followed by increased expansion, 
and decreased heat is followed by decreased expan- 



mill's experimental methods 495 

sion, is all the evidence we need that there is a 
causal connection between the two occurrences. It 
is by the use of a method such as this in cases like 
the last that precise quantitative variations between 
phenomena may often be made out. We may, that 
is to say, measure the increases and decreases in 
amounts of accompanying phenomena, and deter- 
mine the exact correlation between them. Some- 
times only one of the quantities can be measured, 
as, for instance, the correlation between the inten- 
sity of a stimulus and the resulting sensation which 
is formulated in what is known as Weber's law. 
Whenever we experiment with variations of quantity 
in accompanying phenomena, it should be observed, 
in general, that the greater the number and variety 
of the instances in which the correlation is known 
to hold, the greater the certainty that attaches to a 
given conclusion. The desirability of extending our 
observation of accompanying variable phenomena 
over a considerable range of instances is further 
emphasised by the fact that only in this way can 
we determine the limits within which their correla- 
tion holds good. In this way, for example, the upper 
and lower limits of the correlation between intensity 
of stimulus and sensation in each of the sense fields 
has been ascertained. Beyond these limits, the cor- 
relation no longer holds good either because the phe- 
nomenon changes its character or ceases altogether. 
Notwithstanding the necessity for exercising care 
in the use of this Method, it is particularly service- 
able in those cases in which the amounts of varia- 



496 A TEXT-BOOK OF LOGIC 

tion can be measured. "Although," as Mill re- 
marks, "the most striking applications of the 
Method of Concomitant Variations takes place in 
the cases in which the Method of Difference, strictly 
so called, is impossible, its use is not confined to 
those cases; it may often usefully follow after the 
Method of Difference, to give additional precision 
to a solution which that has found. When by the 
Method of Difference it has first been ascertained 
that a certain object produces a certain effect, the 
Method of Concomitant Variations may be usefully 
called in to determine according to what law the 
quantity or the different relations of the effect fol- 
low those of the cause." 

The Method of Residues. Most of the phenomena 
with which the sciences have to deal are complex. 
The experimental methods, as they have been for- 
mulated by Mill, are, as we have seen, statements 
of ways that have been devised for the purpose of 
analysing various kinds and degrees of complexity 
in the material facts that constitute the subject- 
matter of the particular sciences. We have seen 
that when particular phenomena do not conform to 
the requirements of either of the fundamental 
Methods of Agreement or of Difference, the joint use 
of these Methods is then often necessary if we are 
to determine whether and, if so, in what respects, 
phenomena are causally connected. Sometimes our 
analysis of phenomena by this Method enables us 
merely to show that complexes are probably con- 



Mill's experimental methods 497 

nected together in a causal way. We may find, for 
example, in the series of instances: 

POSITIVE INSTANCES 

[ABCD x y z w] 

Antecedents -J \- Consequents 

[A B E F x y v uj 

NEGATIVE INSTANCES 

[BCDE y z w u] 

Antecedents i }► Consequents 

[C F G H z u t sj 

that the negative instances confirm what the positive 
instances suggest, namely, that AB and xy are, in all 
probability, causally related. But the Method itself 
does not, in this case, enable us to analyse the phe- 
nomenon further to determine whether A is causally 
connected with x or not. If, however, we supple- 
ment the Joint Method by the Method of Concom- 
itant Variations, we may be able, by varying A 
or x, to ascertain whether the two phenomena 
are related as cause and effect. It is obvious, 
further, that we may employ the same Method 
for the purpose of ascertaining whether, in the 
above instances, B is causally connected with y, 
and C with z. Now, if experiment should show 
that A and x, B and y, C and z are causally connected 
then, the Method of Residues, which we have to 
discuss, assures us that the remaining phenomena, 
namely D and w, are also causally connected. Thus, 

32 



498 A TEXT-BOOK OF LOGIC 

the Method virtually says that any remainder which 
is left over after other portions of a complex phe- 
nomenon have been explained, are themselves 
causally connected. Mill's statement is as follows: 
Subduct from any phenomenon such part as is known 
by previous inductions to be the effect of certain ante- 
cedents, and the residue of the phenomenon is the 
effect if the remaining antecedents. 

The Method of Residues, as it has just been 
stated, is constantly employed in the sciences. To 
take one illustration only, as this is given by Jevons. 
"In chemical analysis," he writes, "this method is 
constantly employed to determine the proportional 
weight of substances which combine together. Thus 
the composition of water is ascertained by taking 
a known weight of oxide of copper, passing hydro- 
gen over it in a heated tube, and condensing the 
water produced in a tube containing sulphuric acid. 
If we subtract the original weight of the condensing 
tube from its final weight, we learn how much water 
is produced; the quantity of oxygen in it is found 
by subtracting the final weight of the oxide of 
copper from its original weight. If we then sub- 
tract the weight of the oxygen from that of the 
water, we learn the weight of the hydrogen which 
we have combined with the oxygen. When the 
experiment is carefully performed ... we find that 
88.9 parts by weight of oxygen unite with 11.11 
parts of hydrogen to form 100 parts of water." 

Mill calls our attention to the fact that the 
Method of Residues is specially serviceable in those 



mill's experimental methods 499 

cases where several causes acting together produce 
an effect which is the joint result of all the causes 
taken together. In such cases, we have, what Mill 
calls, an "intermixture of effects." What is meant 
by an intermixture of effect has been explained by 
Jevons as follows: "If in one experiment friction, 
combustion, compression, and electric action are all 
going on at once, each of these causes will produce 
quantities of heat which will be added together, and 
it will be difficult or impossible to say how much 
is due to each cause separately. We may call this 
a case of the homogeneous intermixture of effects, 
the name indicating that the joint effect is of the 
same kind as the separate effects. There are several 
causes, each producing a part of the effect, and we 
want to know how much is due each." What is here 
called by Jevons a homogeneous intermixture of 
effects, Mill also called a Composition of Causes. He 
writes : "I shall give the name of the Composition 
of Causes to the principle which is exemplified in 
all cases in which the joint effect of several causes 
is identical with the sum of their separate effects." 
In contradistinction to the case just mentioned, the 
intermixture of effects may also be heterogeneous 
when, as Mill says, "the agencies which are brought 
together cease entirely, and a different set of phe- 
nomena arise: as in the experiment of two liquids 
which, when mixed in certain proportions, instantly 
become, not a larger amount of liquid, but a solid 
mass." 



500 A TEXT-BOOK OF LOGIC 

We may remark, further, that the Method of 
Residues is significant because it operates in the 
interests of thoroughness in scientific observation. 
It sets a barrier against carrying over into science 
the popular attitude towards what is small and 
insignficant, and its use has taught the scientist 
that what appears small and insignficant if often 
the hinge upon which scientific discoveries of the 
first important turn. "Almost all the greatest dis- 
coveries in astronomy,' ' says Herschel, "have re- 
sulted from the consideration of residual phenomena 
of a quantitative or numerical kind. . . It was thus 
that the grand discovery of the Procession of the 
Equinoxes resulted as a residual phenomenon, from 
the imperfect explanation of the return of the sea- 
sons by the return of the sun to the same apparent 
place among the fixed stars." The discovery of the 
planet Uranus, to which we have referred in an- 
other connection, and the invention of the steam 
engine, are other instances of the importance of 
paying attention to residual phenomena. What one 
calls 'luck' in ordinary life, what one calls 'genius' 
in scientific life, and what one calls 'success' in 
commercial life are all of them very often merely 
the result of giving heed to details that the average 
person passes lightly by. In this regard, the fol- 
lowing quotation from Darwin's 'Life and Letters' 
has its value. "A point apparently slight and un- 
connected with his present work is passed over by 
many a man almost unconsciously, with some half- 
considered explanation, which is really no explana- 



MILL'S EXPERIMENTAL METHODS 501 

tion. It was just these things that he (Darwin) 
seized upon to make a start." 

REFERENCES 

H. A. Aikins, The Principles of Logic, Chs. XXVI., XXVII., 
XXIX. 

J. E. Creighton, An Introductory Logic, 3d Edition, Chs. 
XVI., XVII. 

S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
tion, Ch. IX., §§3-9. 

W. Minto, Logic, Inductive and Deductive, Book II., Chs. IV., 
V., VI. 

C. Read, Logic, Deductive and Inductive, 3d Edition, Ch. 

XVI. 

ADVANCED 

W. R. B. Gibson, The Problem of Logic, Ch. XLV. 
L. T. Hobhouse, The Theory of Knowledge, Chs. XIII., XIV., 
XV. 

D. Hume, Treatise of Human Nature, Book L, Part III., § XV. 
H. W. B. Joseph, An Introduction to Logic, Ch. XX. 

H. Lotze, Logic, Book II., Ch. VII. 

J. S. Mill, A System of Logic, Book III., Chs. VIII., IX. 

C. Sigwart, Logic, Vol. II., Part III., Ch. V., § 95. 

QUESTIONS 

1. State briefly the relation of Mill's 'Logic' to the history 
of inductive logic in the modern era. 

2. With what problem does Mill's chapter on 'The Four 
Methods of Experimental Inquiry' deal? 

3. What is meant by calling causal relations reciprocal? 

4. Are all causal relations reciprocal? Explain. 

5. What relation have Mill's Methods to the special modes 
of inquiry developed by each science to meet its own 
problems? 



502 A TEXT-BOOK OF LOGIC 

6. Explain as well as you can exactly what Mill's Methods 
undertake to do. 

7. In what sense can it be said that Mill's Methods rest 
upon a process of elimination? 

8. What is Joseph's view of elimination as applied to 
causal problems? 

9. What view, according to Gibson, does Mill take of the 
nature of elimination? 

10. What is the characteristic feature of the Method of 
Agreement? 

11. What is Jevons' formulation of Mill's Method of Agree- 
ment? 

12. What criticisms may be passed on this Method for de- 
manding a point of single agreement among the phe- 
nomena which it examines? 

13. Is the Method of Agreement one of observation or 
explanation? Give reasons for your answer. 

14. What degree of certinty attaches to the conclusions 
reached by the Method of Agreement? 

15. What are the chief features of the Method of Differ- 
ence as formulated by Mill? 

16. What is meant by calling the Method of Difference a 
method of scientific experiment? 

17. How does Mellone formulate the Method of Difference? 

18. What two kinds of instances are presupposed by the 
Method of Difference, and by what names are they 
called? 

19. Why is it necessary to vary only one condition at a time 
in a series of scieintific experiments? 

20. What does Mill mean by a permanent cause? 

21. How does the operation of permanent causes affect the 
applicability of the Method of Difference? 

22. Under what conditions does the Joint Method of Agree- 
ment and Difference become effective? 

23. To what two classes of problems is the Joint Method 
applicable? 



MILL'S EXPERIMENTAL METHODS 503 

24. What are the chief features of the Joint Method as 
formulated by Mills? 

25. Show, by the enumeration of supposed instances to 
which the Methods of Agreement and of Difference do 
not apply, the conditions which call for the use of the 
Joint Method. 

26. What criticism can be made of the way in which Mill 
formulates the Joint Method? 

27. What statement has been given by Mellone of this 
Method so as to avoid such criticism? 

28. Explain carefully and in detail how you would apply the 
Joint Method. 

29. Verify each step of your answer to the previous ques- 
tion by using the analysis of the social example given 
in the text. 

30. What is the Method of Concomitant Variations? 

31. What two classes of cases are presupposed by Mill's 
statement of the Method of Concomitant Variations? 

32. How can you determine which of these two cases is 
present in any particular instance? 

33. On what general principle does the Method of Concom- 
itant Variations rest? 

34. What is the relation of this Method to that of Differ- 
ence? How is it affected by the operation of permanent 
causes? 

35. In what way does the Method of Concomitant Variations 
enable us to determine causal relations between quan- 
titative phenomena? 

37. Illustrate how the measurements of quantitative phe- 
nomena enable us to determine causal relations, first, 
in instances where both antecedent and consequent can 
be measured, and, second, where only antecedent can be. 

38. What, according to Mill, are the chief uses of the 
Method of Concomitant Variations? 



504 A TEXT-BOOK OF LOGIC 

39. State briefly the relations of the Methods of Agreement 
and Differences, the Joint Method, and the Method of 
Concomitant Variations to one another with a view to 
shrow what Mill means by the Method of Residues. 

40. Illustrate the Method of Residues. 

41. What does Mill mean by the intermixture of effects? 

42. Why should the Method of Residues be specially applic- 
able to cases which involve an intermixture of effects? 

43. In what way does the Method of Residues operate in 
the interests of thoroughness in scientific observation? 

EXERCISES 

1. Examine each of the examples of inductive reasoning 
given below, and state by what method or combination 
of methods the conclusion in each case is reached. 

(1) It is found that sun-lit air has been the means of 
eliminating some diseases, and of diminishing the 
severity of a number of others; whence it seems 
to follow that for maintaining a high degree of 
health sun-light air is essential. 

(2) Other conditions remaining the same, children who 
are taught in classes which average from twenty 
to twenty-five in number attain in the same amount 
of time a higher degree of proficiency than those 
taught in classes which average from forty to fifty, 
or attain the same degree of proficiency in a 
shorter amount of time. 

(3) Sachs maintained, in 1862, that starch is formed 
by the decomposition in chlorophyl of carbon- 
dioxide gas under the influence of light. He found 
that when all other conditions were constant, and 
light was excluded from a plant, no starch was 
formed; the single circumstance of readmitting 
light was accompanied by renewed formation of 
starch. Further, he found that if certain portions 



mill's experimental methods 505 

of the leaves of an illuminated plant were covered 
with black paper, no starch was found in these 
portions. 

(4) Tyndall found that of twenty-seven sterilised flasks 
containing infusion of organic matter, and opened 
in pure Alpine air, not one showed putrefaction; 
while of twenty-three similar flasks, opened in a 
hay loft, only two remained free from putrefaction 
in three days. He concluded that putrefaction is 
due to floating particles in the air. 

(5) In 1675 Leeuwenhoek discovered infusoria, or ani- 
malculae under the microscope, and it was thought 
that such minute organisms as these might be 
spontaneously generated, even if the larger were 
not. About 1745 Needham performed a number 
of experiment to test this conclusion. He extracted 
the juices of meat by boiling, enclosed them in 
bottles, which were carefully corked and sealed 
with mastic, then subjected the closed bottles to 
heat and set them away to cool. In due course of 
time, the fluids thus treated became infected with 
microscopic life, and inasmuch as he believed that 
he had killed all living germs by repeated heating, 
he concluded that the living forms had been pro- 
duced by spontaneous generation. 

(6) Spellanzi, however, thought that Needham's ex- 
periments had not been conducted with sufficient 
care. He, therefore, made a great number of sim- 
ilar experiments, using different kinds of infusions. 
But he placed them in thin flasks with slender 
necks, which were then hermetically sealed in 
flame, after which he immersed the flasks in boil- 
ing water for three-quarters of an hour, in order 
to destroy all germs that might be contained in 
them. Under these conditions no infusoria ap- 



506 A TEXT-BOOK OF LOGIC 

peared in them. Needham was not satisfied with 
these results, however, and objected that such pro- 
longed boiling would destroy not only germs, but 
the generative force of the infusion itself. Spell- 
anzi easily disposed of this objection by showing 
that when the infusions were again exposed to the 
air, no matter how severe or prolonged the boiling 
to which they had been subjected, the infusoria re- 
appeared. 

(7) Goldschneider proved that muscular sensations 
play no considerable part in our consciousness of 
the movement of our limbs, by having his arm sus- 
pended in a frame and moved by an attendant. 
Under these circumstances, where no work de- 
volved on his muscles, he found that he could dis- 
tinguish as small an angular movement of the arm 
as when he moved and supported it himself. 

(8) The case has been supposed of a man who, having 
a taste for cucumber, attributes his chronic indi- 
gestion now to the salmon, now to the cheese, now 
to the pastry — no one of which is an invariable 
feature of his evening meal — but never to the 
cucumber, which he takes every evening. However, 
after having dined without cucumber on several 
consecutive evenings, whilst taking salmon one 
evening, pastry the next, and so on through the 
whole list of suspicious dishes, he cannot but notice 
that on no one of these evenings did any indiges- 
tion occur, and is thus brought to confess that the 
cucumber, after all, must have been the offending 
cause. 

(9) Ferri, in his Criminal Sociology, writes: I have 
shown that in France there is a manifest corre- 
spondence of increase and decrease between the 
number of homicides, assaults and malicious 



MILL'S experimental methods 507 

wounding, and the more or less aboundant vintage, 
especially in the years of extraordinary variations, 
whether of failure of vintage (1853-5, 1859, 1867, 
1873, 1878-80), attended by a remarkable diminu- 
tion of crime (assault and woundings), or of abun- 
dant vintages (1850, 1856-8, 1862-3, 1865, 1874-5), 
attended by an increase of crime. 



CHAPTER XVIII 

FALLACIES 

Fallacy Defined. The earliest systematic account 
of fallicies was given by Aristotle in his treatise 
was on sophistical arguments (-n-epl o-o^io-tikwv ikeyxw). 
The aim of this treatise was to name and examine 
the various tricks that were relied on by many of 
the sophists to win the applause of their audience. 
We may say, therefore, that it contains an exami- 
nation of the various forms of 'sophistry' current 
among the Greeks of the fourth century B. C. To 
this practical employment of the term corresponds, 
in a general way, the meaning that must be assigned 
to it when, at the present day, it is used in a popular 
sense. From this point of view, a fallacy may be 
said to be any error of statement or belief. If, for 
example, any one should believe that the sun revolves 
around the earth, such a belief would be called fal- 
lacious, and the statement of that belief would 
be called a fallacy. This meaning of the word, 
however, is too indefinite for the purposes of logic, 
and it covers too miscellaneous a group of cases to 
be of much service in directing its inquiries. It 
is customary, therefore, to narrow the interpreta- 
tion of the term by confining its application to any 
breach of the principles and rules of logical pro- 
cedure. In the foregoing pages, we have become 
acquainted with a number of the principles and 

(508) 



FALLACIES 509 

rules to which we must submit our thought and our 
speech if what we assert and what we express are 
to carry logical conviction. And, doubtless, our 
study of these principles and rules, and our effort 
to put them into practice, have convinced us both 
of the necessity and of the difficulty of conforming 
our thought and speech to their requirements. Now 
whenever our thinking fails to conform to such 
principles and rules, we are said, in the strict sense 
in which the term is used in logic, to be guilty of a 
fallacy. A fallacy, therefore, may be denned as any 
breach of a logical principle or rule. 

This statement of what we understand in logic 
by a fallacy needs to be safeguarded in one par- 
ticular. As it stands, and especially if one does 
not regard strictly the context in which it occurs, 
it will seem capable of including, not only those 
breaches of logical procedure to which the definition 
is intended to confine it, but also those errors which 
arise from other than logical sources, and to which 
the term fallacy can be applied only in a popular 
and conventional sense. There are, no doubt, nat- 
ural limitations of mind which prevent all of us 
at some time from attaining, in the character of our 
intellectual life, anything that can be called with 
propriety logical exactness. Indeed, the ordinary 
course of life, as we have so often said, does not 
depend for the attainment of its objects on the 
strictness with which logical requirements are met 
in the field of the interests by which that life is 
controlled. And, doubtless, mistakes occur here 



510 A TEXT-BOOK OF LOGIC 

which have their roots in the mental process by 
means of which that life is carried on. We have 
pointed out, for instance, that perception does not 
provide a secure foundation of knowledge, and if 
we were to add that the organisation of our ordi- 
nary experience proceeds very largely upon prin- 
ciples of association, it would be evident, in the 
light of our previous studies, that association cannot 
guarantee against logical error the conclusions to 
which it is the means of conducting us. In so far, 
then, as we have regard to the mistakes that arise 
in this field, it would be quite misleading to apply 
the term fallacy to these mistakes, and they must 
be considered as falling outside the scope of our 
definition. We may point out also that lapses into 
this more usual method of procedure are likely to 
occur in the course of our efforts to reach more 
strictly scientific results. The exclusion of these 
cases from the field of the fallacies is made on the 
principle that such cases do not involve ignorance 
of the methods of logical procedure, but carelessness 
in their application; just as, for example, ignorance 
of a mathematical rule would not be attributed to 
one whose mistake was obviously due to haste or 
inattention in its application to a given case. We 
must regard as logical fallacies, therefore, only 
those instances of erroneous conclusions which rest 
upon grounds which are demonstrably false. It is 
in this sense, then, that a fallacy was defined above 
as any breach of a logical principle or rule. 



FALLACIES 511 

Classification of Fallacies. Although Aristotle 
was limited in his treatment of fallacies by the 
practical purpose to which reference has been made, 
and although he had before him chiefly those errors 
to which the Sophists were exposed by their desire 
for popular favour, his classification of fallacies 
has remained the basis of what may be regarded in 
logic as the traditional position on this subject. In 
the work referred to, Aristotle divided fallacies into 
two main classes, a division which corresponds, in a 
general way, to the distinction on which we have in- 
sisted in our discussions of logical doctrine, the dis- 
tinction, namely, between truth in the form of judg- 
ments, and truth expressed in the form of proposi- 
tions. According to this distinction, fallacies may 
arise from the way in which we express or interpret 
propositions, or, as Aristotle said, they may be due 
directly to language (irapa rty \4£iv; in dictione) ; or 
they may exist in the thoughts or judgments that 
we assert, or, as Aristotle expressed it negatively, 
they may not be due to the language we employ 
(f£» rij<; \e£e<o*; extra dictionem). Under the first 
class Aristotle enumerates six kinds of fallacy, some 
of which are trifling and dependent wholly on the 
syntax of the Greek language ; and under the second 
class, he enumerates seven. Beyond the distinction 
of these two main classes we are not directly inter- 
ested in Aristotle's classification. 

There is, perhaps, no entirely satisfactory class- 
ification of fallacies, and the most that can be 
attempted here is to bring under some practical and 



512 A TEXT-BOOK OF LOGIC 

intelligible scheme the various errors to which log- 
ical thinking is exposed. It will help us to do this 
if we recall, in the first place, that the proposition 
was said to be an expression in words of the truth 
asserted in a judgment. We saw that, for the per- 
son speaking, the problem was to find words which 
express adequately the thought that he desires to 
convey, and, for the person spoken to, it was to 
interpret the words in which a judgment is ex- 
pressed in the sense that they had for the person 
who first used them as the embodiment of an idea. 
In either case, the logical value of a proposition 
depends to a large extent on language, on the fitness 
of the verbal forms which are chosen as the medium 
of ideas. If one realises the great difficulty, which 
the masters of literature alone have at all adequately 
overcome, of choosing words that reveal the mean- 
ing their employment is intended to convey, he will 
understand why logicians, since Aristotle, have con- 
tinued to regard language as one main source of 
logical fallacy. The study of the fallacies which 
beset our interpretation of propositions through 
the ambiguous use of language will form for us the 
first group of fallacies. 

Our second main group of fallacies will comprise 
those mistakes which threaten our comprehension 
of the full meaning of propositions. It will be 
remembered that we pointed out that our relation 
to propositions is two fold. In the first place, prop- 
ositions need interpreting, and, as we have just now 
intimated, the difficulties in the way of interpreting 



FALLACIES 513 

propositions constitutes the first main class of fal- 
lacies. But, in the second place, it was pointed out 
that propositions contain implications which limit 
in certain determinate directions what we can think 
about the subject-matter of their assertion. For 
instance, we said that if we admit the truth or 
falsity of a given proposition we are thereby com- 
mitted to the truth or falsity of a number of other 
propositions. An examination of the possible 
sources of error in this region, the region of logical 
implication, will enable us to avoid one of the most 
frequent pitfalls in the way of that accuracy and 
precision that is the desideratum of the intellectual 
life. 

The fallacies that are included under the two 
heads just mentioned refer to the meaning of prop- 
ositions taken singly, they are the fallacies which 
arise in the field of simple, unmediated assertion. 
When, however, we go beyond this region, and our 
assertions take the more complex forms that we 
have studied in the syllogism and induction, a 
special group of fallacies has to be recognised, be- 
cause here thought is guided in its efforts to reach 
logically sound conclusions by special principles and 
rules. The mistakes that occur in connection with 
the control of thought by these principles and rules 
will constitute a third main group of fallacies. 

A fourth group of fallacies may be recognised 
if we recall that no logical assertion, whether simple 
or complex, is ever a wholly detached unit, and 

33 



514 A TEXT-BOOK OF LOGIC 

that, if such assertions are to be interpreted cor- 
rectly, they must be brought into relation to the 
contexts out of which their original meaning was 
forged. Every assertion, we have said, implies a 
certain universe of discourse. Now we often find 
that the plausibility of statements and arguments 
depends on suggestions derived from their contexts 
which are not directly related to the truth char- 
acter of the statements and arguments themselves, 
and for these extrinsic reasons are frequently, 
though fallaciously, accepted as true. They are 
cases of this kind that we shall classify under the 
present head. 

For the sake of convenience, we shall refer to 
the four main classes of fallacy that have just been 
distinguished, in the order in which we have con- 
sidered them, as fallacies of interpretation, of im- 
plication, of inference, and of the context. A cer- 
tain latitude must be allowed in the use of this 
classification, as indeed it must of any classification, 
of fallacies. The only justification that any scheme 
can receive is that it brings together, in a way that 
connects with the development of logical doctrine, 
the errors to which we are exposed in our efforts 
to think accurately and convincingly. If, in addi- 
tion, it groups the fallacies in a way that is easily 
remembered, it has a still further advantage. 

Fallacies of Interpretation. • These are due, as we 
have said, to the deceptiveness of the language in 
which propositions are expressed. They all, there- 
fore, fall under the defect of ambiguity. But since 



FALLACIES 515 

ambiguity may attach either to the words or to the 
structure of our statements, we may distinguish 
two classes of error to which our interpretation of 
propositions is exposed. Among the fallacies due to 
verbal ambiguity we may include equivocation, 
accent, composition, division, accident, and converse 
fallacy of accident; and among those due to struc- 
tural ambiguity, amphibole and false parenthesis. 

Verbal Ambiguity. In discussing the fallacies 
that are due to verbal ambiguity, we may remind 
ourselves that ambiguity is not identical with mere 
indefiniteness in the meaning of words, and that, 
in view of a certain unavoidable indefiniteness in 
the meanings of the words we employ, propositions 
can attain only a non-ambiguous signification. The 
principle of non-ambiguity, we said, controlled all 
our efforts after logical exactness both with respect 
to terms and propositions. We cannot, therefore, 
convict of any of the verbal fallacies a proposition 
whose terms are indefinite, if this indefiniteness 
does not spread to the meaning of the proposition 
taken as a whole. When, however, the indefiniteness 
of the parts affects the meaning of the whole prop- 
osition, we have a case that falls under the class 
of fallacies that we are now considering. With this 
reminder, we take up seriatim the several fallacies 
that originate in verbal ambiguity. 

Equivocation, or indefiniteness in the denotation 
or connotation of a term, gives rise to a fallacy 
when either term of a proposition is interpreted in 
a different sense by the speaker and by the person 



516 A TEXT-BOOK OF LOGIC 

spoken to, and this affects the meaning of the prop- 
osition as a whole ; or when, for the same individual, 
any term which appears in a continuous discourse 
fails to retain the same meaning in the various 
propositions in which it occurs, and this affects 
the conclusion to which one is led. The latter is, 
perhaps, the more usual, as it is, certainly, the more 
insidious, form of the fallacy of equivocation. Any 
form of continuous address, and especially of public 
address, exposes one to the danger of equivocation, 
and the most careful writers sometimes fall into it. 
A familiar example is the following taken from 
MilPs argument in support of the position that hap- 
piness is the chief aim or good of life. He says, 
"The only proof capable of being given that an 
object is visible is that people actually see it. The 
only proof that a sound is audible is that people 
hear it. And so of the other sources of our expe- 
rience. In like manner, I apprehend, the sole evi- 
dence it is possible to produce that anything is 
desirable is that people do actually desire it." For 
the purpose of his argument, the word desirable 
must have the meaning 'worthy to be desired/ but 
this is a meaning that is not analogous to visible 
and audible in the context. Visible and audible 
mean able to be seen or heard, and, therefore, all 
that Mill has a right to argue is that desirable 
means 'able to be desired.' But from this meaning 
he could not argue that happiness is the summum 
bonum or chief good of life, for the fact that a 
person desires an object is no proof that it is, in the 



FALLACIES 517 

sense Mill uses the word, the most desirable. 
Against committing or being imposed on by the 
fallacy of equivocation we may submit the meanings 
of our terms to the methods of translation and defi- 
nition, as these terms have been explained above. 

Accent. The fallacy of accent is any misconcep- 
tion due to the emhasis placed on a word or group 
of words in a sentence. It was for Aristotle the 
mistaken accentuation of a word in writing Greek. 
"A ludicrous instance of this fallacy/' to quote 
Jevons, "is likely to occur in reading Chapter XIII 
of the First Book of Kings, verse 27, where it is 
said of the prophet, 'And he spake to his sons, say- 
ing, Saddle me the ass. And they saddled him' 
The italics indicate that the word him was supplied 
by the translators of the authorised version, but it 
may suggest another meaning. The commandment, 
Thou shalt not bear false witness against thy 
neighbour,' may be made by a slight emphasis of the 
voice on the last word to imply that we are at liberty 
to bear false witness against other persons." We 
may, however, give certain words or groups of words 
a prominence that does not really belong to them in 
another way. For example, in quoting an author 
we may separate a word from its context, italicise 
a word which was not italicised in the original, or, 
by leaving out qualifying words and phrases, we 
may give certain ideas a prominence which they did 
not have for the author himself. Connected with 
this latter interpretation, the fallacy, as Creighton 



518 A TEXT-BOOK OF LOGIC 

observes, "appears in connected arguments of any 
kind in which, while the facts are not actually mis- 
stated, certain aspects of them are so disproportion- 
ately dwelt upon and emphasised, at the expense of 
the rest, that a false idea of the subject in its en- 
tirety is the result. In this wider form, this fallacy 
is one that may be described as the particular vice 
of special pleading; and the caution that may be 
suggested against it is, in the language of the 
astronomer, to make allowances for the 'personal 
equation' both in one's own thinking and in that of 
others." 

Composition. The fallacy of composition, like 
its converse, the fallacy of division, turns on the 
distinction between the distributive and collective 
use of terms. This distinction, it will be remem- 
bered, is based on the fact that we may predicate 
qualities and relations of a class without at the 
same time predicating those qualities or relations 
of the individuals that constitute the class; and, 
conversely, we may predicate qualities and relations 
of the individuals that constitute a class without at 
the same time predicating those qualities or rela- 
tions of the class. Now, we are guilty of the fal- 
lacy of composition when, having predicated some- 
thing of a term used distributively, that is, of each 
of the individuals that fall under the term, we sup- 
pose that the predicate belongs to the term in its 
collective sense, that is, of the individuals taken as 
a group. "We must not argue," to use Jevons' illus- 



FALLACIES 519 

trations, ''that because every member of a jury is 
very likely to judge erroneously, the jury as a whole 
is also very likely to judge erroneously; nor that be- 
cause each of the witnesses in a law case is liable to 
give false or mistaken evidence, no confidence can 
be reposed in the concurrent testimony of a number 
of witnesses. It is by a fallacy of Composition that 
protective duties are still sometimes upheld. Be- 
cause any one or any few trades which enjoy pro- 
tective duties are benefited thereby, it is supposed 
that all trades at once might be benefited similarly ; 
but this is impossible, because the protection of one 
trade by raising prices injures others.'' 

Division. The fallacy of division is, as was said, 
the converse of the fallacy of composition. It was 
so considered by Aristotle. It occurs when we sup- 
pose that a statement that is true of a group is true 
of the individuals of the group. If, for example, 
it is true that a particular class of college students 
are bright, it does not follow that this is true of 
each or any particular one of the members of the 
class, any more than it follows that because a jury 
can be relied on to reach a just verdict that a sim- 
ilar confidence can be placed in any one of the jury- 
men. Gibson has called attention to an interesting 
illustration of this fallacy to be found in Thomas a 
Kempis' Imitatio Christi. In the paragraph refer- 
red to, the writer is exhorting the 'good monk' not 
to seek any earthly delight, but to remain alone in 
his cell. The argument by which this advice is sup- 
ported reads: "What canst thou see elsewhere 



520 A TEXT-BOOK OF LOGIC 

which here thou seest not? Behold the sky and the 
earth, and all the elements, for of these are all 
things made." Expressing this argument syllogis- 
tically, Gibson detects the fallacy of division in the 
middle term. Thus: 

The elementary substances (in organised combination) 

are the whole material world. 
The objects included in the prospect from your cell are 

the elementary substances (not so combined). 
Therefore, the objects included in the prospect from your 

cell are the whole material world. 

As this ilustration suggests, the fallacy of division, 
in common with many others, is most liable to occur 
in continuous discourse, and the value of putting 
the subject-matter of such discourse into the logical 
forms suitable to them is that we may the more 
easily detect any fallacy lurking in our thought, or 
in the forms in which that thought is expressed. 

Accident. The fallacy of accident occurs when 
we suppose that what is true of a term used in a 
relatively indeterminate or unconditioned sense, is 
true of the term when used in a relatively deter- 
minate or conditioned sense. The Latin name of 
the fallacy is, Argumentum a dicto simpliciter ad 
dictum secundum quid. It is, that is to say, a tran- 
sition from what is true of an indeterminate state- 
ment to what is true of the same statement 'with a 
modification.' In other words, it consists in secur- 
ing assent to a statement in a general form, and 
then proceeding as if it held under some special 



FALLACIES 521 

circumstance. If we supposed, for example, that 
because it is right for a man to inculcate his own 
opinions, it is, therefore, right for a magistrate to 
use his position to enforce his own political views, 
we should be guilty of this fallacy. For, as Mellone, 
from whom this illustration is taken, remarks, "we 
cannot infer of his special powers as a magistrate 
what is only true of his general rights as a man." 
We may often detect the fallacy in our thoughts 
about moral questions. Thus, in discussing such 
questions, "one may insist that all men by nature 
seeks after the good, meaning that each man acts 
sub specie boni, and is therefore seeking after some 
kind of good, even when he is pursuing his own 
pleasure. But, in continuing the argument, he may 
use the term 'good' in a differentiated sense — e. g., 
in the sense of the common good, or the good of 
humanity — and come thereby, through a fallacy of 
accident, to the conclusion that all men by nature 
seek the general good." 

The Converse Fallacy of Accident occurs when 
we suppose that what is true of a term used in a 
determinate or conditioned sense is true of the term 
when used in an indeterminate or unconditioned 
sense. The Latin name of the fallacy is, Argumen- 
tum a dicto secundum quid ad dictum simpliciter. 
The following illustrations will be sufficient to make 
the nature of this fallacy obvious. For example, 
let us suppose that it can be shown that the syllo- 
gism is of no use in the discovery of new truth, are 
we warranted in supposing, as the early modern 



522 A TEXT-BOOK OF LOGIC 

critics of the syllogism seem to have done, that it 
is, therefore, of no use whatever ? Or, if philosophy 
'bakes no bread,' is it, therefore, useless? The 
affirmative answer to both these questions involves 
the converse fallacy of accident. 

Structural Ambiguity. In the chapter on the 
proposition, it was pointed out that particular 
statements are often ambiguous, not because the 
terms in which they are expressed are ambiguous, 
but because the structure of the sentences in which 
ideas are expressed are so. It is to the grammatical 
structure of sentences, for example, that we must 
attribute, in part, the difficulty sometimes expe- 
rienced in determining the subject and predicate 
terms of given propositions. Whenever syntactical 
relations obscure the meaning of sentences or para- 
graphs, there is presented a hindrance to the correct 
interpretation of propositions. Difficulties of the 
kind in question are more possible in the classical 
languages where the word order in sentences is 
more variable, and where oblique constructions are 
more common, than in English; but something of 
the same sort is seen in English poetry in which a 
departure from the relative simplicity of the ordi- 
nary prose sentence is often made necessary by the 
demands of metrical composition. 

Amphibole. Now, whenever the structure of the 
sentences in which ideas are expressed, in prose 
or in poetry, leads to opposed interpretations of 
such sentences, we have the typical fallacy of amphi- 
bole. Sometimes sentences whose structure renders 



FALLACIES 523 

their interpretation difficult, although not neces- 
sarily ambiguous, are spoken of as amphibolic. 
This is a view similar to that sometimes taken of 
words, when any degree of indefiniteness is thought 
sufficient to render them equivocal. This seems to 
us too loose an interpretation of these fallacies. As 
we have pointed out in regard to words, there is 
also a certain freedom in the use of syntactical 
relations that is allowable and necessary if partic- 
ular shades of meaning are to get expressed in the 
sentences we employ. The object that the transla- 
tion of sentences into propositions keeps in view 
is, not to give all statements an equal clearness, but 
to bring out the exact degree of clearness that be- 
longs to each of our statements. A certain indefi- 
niteness of meaning may be characteristic of propo- 
sitions, therefore, without involving them in the 
fallacy of amphibole. Before we can convict any 
statement of being amphibolic, we must have ex- 
hausted all the means at our disposal to interpret 
the statement, and to give it an expression which 
truly represents its meaning. If it then remains 
ambiguous, if, that is, our attempt to give the state- 
ment a propositional form is defeated on account of 
its equivocal syntax, we may properly regard it as 
an example of the fallacy of amphibole. An illus- 
tration of this statement may be found in the often 
quoted lines of Shakespeare, 'The Duke yet lives 
that Henry shall depose.' We are baffled in any 
attempt to put this sentence into the form of a 
proposition, because its structure does not enable 



524 A TEXT-BOOK OF LOGIC 

us to determine whether it means, 'The Duke yet 
lives who shall depose Henry/ or, 'The Duke yet 
lives who shall be deposed by Henry/ Such a 
statement, therefore, is essentially amphibolic. The 
student will recall, in further illustration, many of 
the utterances of the oracles, for instance, 'If 
Croesus should wage war against the Persians, he 
would destroy a mighty empire/ As further ex- 
amples we may cite, 'It is possible for thee the 
enemy to overcome,' 'The lion David slew.' 

False Parenthesis. Closely connected with the 
foregoing, is the fallacy of false parenthesis. It 
consists essentially in an uncertainty with regard 
to the relations of the main and subordinate clauses 
of a sentence. For example, 'I ruined the cause 
and injured my own prospects which I deeply re- 
gret/ a statement that may mean either, 'I ruined 
the cause, and injured my own prospects which I 
deeply regret/ or, 'I ruined the cause and injured 
my own prospects, which I deeply regret/ A sim- 
ilar fallacious statement is 'I will begin and finish 
the task tomorrow/ The advertising columns of 
our newspapers are sometimes said to provide us 
with humorous illustrations of the fallacy of paren- 
thesis. For instance: 

Lost — A valuable silk umbrella belonging to a gentle- 
man with a curiously carved head. 

Wanted — A groom to look after two horses of a pious 
frame of mind. 

For Sale — A Newfoundland dog; will eat anything, 
particularly fond of children. 



FALLACIES 525 

We introduce these instances, not in order to 
subscribe to the view that they are amphibolic in 
character, but to point out that if these are to be 
admitted as examples of amphiboly, then any badly 
constructed sentence would have to be included 
whether or not their meaning was involved in am- 
biguity. This is a view to which, as we said above, 
we cannot subscribe. 

Fallacies of Implication. The second main class 
of fallacies which we have now to consider com- 
prises those that occur when for any reasons we 
mistake the implications of propositional state- 
ments. The difficulties that confront our efforts to 
give to any statement a propositional form have 
been considered already, and in contrast to these, 
the ones with which we are now concerned presup- 
pose that those difficulties have been overcome, and 
that we know unequivocally the significance that 
particular statements have. Until we are sure what 
the asserted meaning of a proposition is, we cannot 
raise the question whether, and if so what, further 
or implied meaning it can have. 

It will be remembered that by implication is 
meant the unexpressed signification of a logical 
proposition, and that implications may assume one 
or the other of two forms. In the first form, the 
unexpressed or implied propositions may be related 
to the given proposition in the way of opposition, 
in the second form, they may be related to the 
given proposition in the way of eduction. These 



526 A TEXT-BOOK OF LOGIC 

distinctions will provide us a natural and easy 
method of classifying the fallacies of implication. 

Fallacies of Opposition occur when, from state- 
ments accepted as true or false, other statements 
dealing with the same subject-matter are derived, 
the truth or falsity of which is, mistakenly, sup- 
posed to rest upon the principles that determine the 
relations of opposed propositions. It has been 
shown above that there are four kinds of relation 
between propositions in opposition, — contrariety, 
subcontrariety, subalternation, and contradiction. 
These relations have been studied, and the propo- 
sitions between which each obtains have been indi- 
cated. In view, therefore, of what we have learned 
with respect to this class of implication, it is readily 
seen that, in respect to this class, our thought be- 
comes fallacious when we suppose that the prin- 
ciples of opposition justify a statement which, as 
a matter of logic, they are incapable of support- 
ing. Or, to put it another way, any statement 
which avowedly rests upon the principles of opposi- 
tion is fallacious if it can be shown that those prin- 
ciples fail to give it the necessary support. 

In general, it is quite obvious that there are as 
many fallacies of opposition as there are pairs of 
propositions between which relations of opposition 
may hold. Some of these relations are in themselves 
so obvious, the relation of contradiction, for in- 
stance; and others lose so readily whatever obscur- 
ity they may have when they occur between certain 
pairs of propositions, that it is not necessary to 



FALLACIES 527 

consider all the possible fallacies of opposition. All, 
therefore, that we shall attempt is to point out 
some of the difficulties that may be experienced in 
the effort to conform our thinking to the principles 
of opposition. 

And, in the first place, we may consider the 
fallacy of contrariety which occurs when we sup- 
pose that the falsity of one universal proposition, 
A or E, involves the truth or falsity of the other, 
E or A. It may be false, for example, that 'None 
of the members of the team are bona fide students/ 
but it does not , therefore, follow that 'All the 
members of the team are bona fide students/ 
and it does not follow because, it might still be 
true that 'Some of the members of the team are not 
bona fide students/ It is certainly very easy for 
the untrained mind to proceed from the falsity of a 
universal to the truth of its logical contrary, and 
one is particularly exposed to this error when the 
latter statement is separated in our discourse from 
the former by an appreciable lapse of time. But, 
as we saw above, the statement of what is false in 
a universal form does not enable us to say anything 
with respect either to the truth or falsity of its 
contrary. In such cases the contrary is always in- 
volved in doubt. 

In the second place, we are exposed to a 
fallacy of sub contrariety when we attempt to argue 
from the truth of a particular proposition, I or 
0, to the falsity of another particular proposition, 
or I. We run into this error when we forget 



528 A TEXT-BOOK OF LOGIC 

that two particular propositions dealing with the 
same subject-matter, one of which is affirmative 
and the other negative, may both be true. From the 
statement, for example, that 'Some of those who 
have given their word are keeping it faithfully/ it 
does not follow that 'Some of those who have given 
their word are not keeping it faithfully' is false, 
since this latter statement might be true of any of 
those not included in the original statement. 

In the third place, fallacies of sub alternation may 
arise when we argue either from the falsity of a 
universal propostion, or from the truth of a par- 
ticular proposition. The falsity of a universal propo- 
sition, 'All that I have done for you has gone for 
nought/ might very well seem to involve the falsity 
of the particular subaltern, 'Some of the things I 
have done for you have gone for nought/ but this 
would not necessarily be the case, because the truth 
or falsity of the subaltern proposition depends in 
this case upon the degree of falsity of the original 
proposition, and it is exactly this that we cannot de- 
termine from that proposition itself. Unless it were 
so common, one would hardly think it necessary to 
call attention to the other fallacy of subalternation, 
the fallacy, namely, that is involved in proceeding 
from the truth of a particular statement to the truth 
of its corresponding universal. It may, for example, 
be quite clear that from the statement that 'Some 
books are dull/ we cannot proceed to the statement 
that 'All books are dull/ but we dare say, it is not 
equally obvious that we cannot proceed from the 



FALLACIES 529 

statement, 'Some planets move in their own orbits', 
to, 'All planets move in their own orbits.' The rea- 
son why we cannot argue from the truth of a part- 
icular statement to either the truth or falsity of 
the universal of the same quality seems to be that 
we have no means of determining, by an examina- 
tion of the original statement, the precise amount 
of truth that is claimed by it, that is, whether it 
states the whole truth about its subject, or only 
part of it. 

Fallacies of Eduction. Eductions were defined 
above as those relations which propositions dealing 
wity the same subject-matter have to one another 
when they express what is true about this subject- 
matter from different points of view. There are, 
as we said, two fundamental methods for deter- 
mining these relations, obversion and conversion, 
and it is with respect to these methods, therefore, 
that fallacies are likely to occur. An eductive fal- 
lacy may, consequently, be defined as an error of 
implication due to a misunderstanding of obversion, 
of conversion, or of both. 

The fallacy of obversion is most likely to occur 
when for the contradictory of the predicate of an 
original proposition we substitute its contrary in 
the obverse proposition. Now by contrary terms 
we mean those which, although opposed to one an- 
other, do not exhaust between them the particular 
universe of discourse to which they both belong. 
Black and white are, in this sense, contrary, but 
they are not contradictory, terms. By a contra- 

34 



530 A TEXT-BOOK OF LOGIC 

dictory term we mean one that, together with the 
original term, does exhaust the universe of discourse 
to which both terms belong. Thus, black and not- 
black are contradictory, but they are not contrary, 
terms. It is, then, a confusion of contrary with 
contradictory terms, in the sense in which these 
have been denned, that gives rise to the fallacy of 
obversion. Thus, it would be quite fallacious, for 
the reason already assigned, if we supposed that 
we were warranted in saying of a particular indi- 
vidual that he was bad, if all we knew was that he 
is not good; good and bad are contrary, they are 
not contradictory, terms. Again, if we supposed 
that the obverse of the proposition 'He is not happy, 
was 'He is unhappy/ there would be as complete 
misunderstanding of what was implied in the first 
statement as if we supposed that because a certain 
object was not red that it was, therefore, green. 

Fallacies of Conversion are most likely to occur 
in the case of the universal affirmative, and the 
particular negative propositions. In the latter case, 
the fallacy occurs when we suppose that from a 
particular negative proposition anything can be 
asserted merely by converting it. It is quite true, 
for example, that 'Some elements are not liquid/ 
and also that 'Some liquids are not elements/ but 
the one statement does not follow from the other 
by simple conversion. Again, a fallacy of conver- 
sion occurs when we suppose that the universal 
affirmative proposition can be simply converted, a 
supposition that is based on the false assumption 



FALLACIES 531 

that both terms of the proposition are distributed. 
In universal affirmative propositions, as we have 
seen, the predicate terms are undistributed; and, 
consequently, when, through conversion, these terms 
become the subjects of new propositions, these prop- 
ositions must be particular in quantity. The neg- 
lect of this consideration leads directly to a fallacy 
of conversion. 

Fallacies of Inference. The class of fallacies to 
which we now direct attention includes the errors 
to which our thinking is exposed when it is con- 
fronted by the difficulties that are involved in the 
more complex logical processes known as argu- 
ments. The two classes of fallacy already con- 
sidered, the fallacies of interpretation and implica- 
tion, are concerned with the errors to which thought 
is liable when it deals with single statements; but 
it is not until these simpler errors have been avoided, 
not until single statements have been given a strictly 
logical form and content, that there comes into view 
the class of fallacy that is connected with our at- 
tempt to put into their logical relations such logically 
determined propositions. For, in an argument, not 
only must the constituent propositions be free from 
ambiguity, but the relations between these proposi- 
tions must be precisely determined. It is perfectly 
obvious, therefore, that the avoidance of the fal- 
lacies of interpretation and implication is essential, 
if we are to meet and overcome the difficulties that 
are occasioned by the more complex character of 
our thinking in the process of argument. We may, 



532 A TEXT-BOOK OF LOGIC 

therefore, say that just as the avoidance of the fal- 
lacies of interpretation are presupposed by any 
attempt to avoid the fallacies of implication, so the 
avoidance of both these classes of fallacy is presup- 
posed by any attempt to overcome the fallacies of 
inference. 

Arguments, from the time of Aristotle, have 
been recognised to be of two kinds: those, namely, 
that start with the recognition of some general 
principle, and those that start with the collection 
of a number of particular facts. In the former, the 
aim is to bring, through the mediation of a middle 
term, some particular fact under the principle which 
constitutes what is called the major premise of the 
argument; in the latter, it is, through an analysis 
of particular facts, to state a principle that shall 
exhibit what is common to all the facts examined, 
and, if possible, to extend that principle to other 
facts which either have not been examined, or which 
are not known to exist. It is usual to call the 
former kind of argument deductive, and the latter, 
inductive; and, although there is a danger of sup- 
posing, falsely, that they constitute quite separate 
logical processes, we may use these names, deductive 
and inductive, for the purpose of classifying the 
fallacies of inference. The deductive fallacies will 
include those errors that arise in connection with 
the syllogism, and the inductive fallacies will include 
those that arise in connection with the various steps 
through which it is necessary to pass in our efforts 
to establish causal connections. 



FALLACIES 533 

The Deductive Fallacies. Whenever an argument 
starts from the conscious acceptance of a general 
truth about its subject-matter, and proceeds to show 
that some particular fact is a special instance of that 
truth, it is said to be a deductive argument. Now, 
since we accept such general truths as are the 
starting points of deductive arguments in either 
one or the other of three forms, in the forms, 
namely, of categorical, hypothetical, or disjunctive 
propositions, these arguments, as we have seen, 
assume a form and character which corresponds to 
the difference in the method and principle by which 
thought, in each case, proceeds to its conclusion. 
In consequence of this fact, we found it necessary 
to consider categorical arguments, hypothetical 
arguments, and disjunctive arguments separately, 
and to give special attention to the rules by which 
thought, in each type of argument, is controlled. 
It follows, from this statement with respect to the 
various forms of deductive arguments, that the 
deductive fallacies can be classified most conve- 
niently by following the line of cleavage between 
the arguments in connection with which they are 
likely to occur. In the following sections, therefore, 
we shall pass in review what we may call the cate- 
gorical, hypothetical, and disjunctive fallacies, the 
fallacies which occur, or are liable to occur, in those 
types of argument to which similar descriptive 
names have been given. 

Categorical Fallacies may be defined as those mis- 
takes in reasoning which render the conclusions of 



534 A TEXT-BOOK OP LOGIC 

categorical arguments erroneous. These fallacies 
fall conveniently into two groups, according as the 
error lies in the terms, or in the character of the 
proposition of the syllogism. To the former group 
we may assign the fallacies of four terms, and to 
the latter, the fallacies of insufficient premises. 

Fallacies of Four Terms occur as a breach of 
the rule which states that a syllogism must contain 
three, and only three, terms. Their occurrence is 
due to a failure to rid the terms of a syllogism of 
ambiguity. Now, since ambiguity may occur either 
in the connotation or in the denotation of a term, 
and may attach to any one of the terms of a syllo- 
gism, it is evident that the fallacies of four terms 
are of two kinds ; those, namely, which occur when 
the meaning of any of the terms of a syllogism is 
ambiguous, and those which are due to a mistaken 
distribution of any of the terms of a syllogism. 
Among the former, it is usual to call special atten- 
tion to the case of the middle term, but it should 
be remembered that the ambiguity of the major or 
of the minor term may also invalidate an argu- 
ment by giving rise to the fallacy of four terms. 
When the fallacy of four terms invalidates a syllo- 
gism on account of the connotative ambiguity of the 
middle term, it takes the special name of ambiguous 
middle; when an argument is invalid on account of 
a similar ambiguity of the major term, the fallacy is 
called ambiguous major; and when ambiguity in the 
meaning of the minor term destroys the validity of 
an argument, the fallacy is called ambiguous minor. 



FALLACIES 535 

It is not necessary to give illustrations of all these 
fallacies. The following will serve to show the form 
in which they are likely to occur. If, as Jevons 
remarks, we argue "that 'all metals are elements and 
brass is a metal, therefore it is an element/ we 
should be using the middle term 'metal' in two dif- 
ferent senses, in one of which it means the pure sim- 
ple substances known to chemists as metals, and in 
the other a mixture of metals commonly called metal 
in the arts, but known to chemists by the name 
alloy." Or, if we argued "that 'what is right should 
be enforced by law, and that charity is right and 
should be enforced by law' . . . it is evident that 
'right' is applied in one case to what the conscience 
approves, and in another use to what public opinion 
holds to be necessary for the good of society." 

The other type of fallacy which results in break- 
ing an argument under the weight of four terms, 
is due to a disregard of the denotation or distribu- 
tion of the terms of a syllogism. In these cases, the 
erroneous conclusion results from a neglect of the 
extent of a term's meaning, rather than to a dis- 
regard of the meaning itself. In other words, it is 
a fallacy of the division, not a fallacy of the defi- 
nition, of a term. Now, as we have seen, the dis- 
tribution of the terms of a syllogism is subject 
to special rules. In respect of the middle term, the 
rule states that this term must be distributed in one, 
at least, of the premises ; and in respect of the major 
and minor terms, the rule states that if either of 
these terms is distributed in the conclusion, it must 



536 A TEXT-BOOK OF LOGIC 

have been distributed in the corresponding premise. 
When the rule relating to the middle term is dis- 
regarded, the resulting fallacy is known as undis- 
tributed middle; and when the rule relating to the 
terms of the conclusion is disregarded, the resulting 
fallacy, in the case of the major term, is known as 
illicit process of the major, and, in the case of the 
minor, as illicit process of the minor. The fol- 
lowing illustrations will throw light on these state- 
ments. If we should argue, for example, that be- 
cause "all rash men are confident, and all brave men 
are confident," therefore, "all rash men are brave," 
we should be guilty of the fallacy of undistributed 
middle. Again, if we argued "that 'because many 
nations are capable of self-gvoernment, and and 
that nations capable of self-government should not 
receive laws from a despotic government, therefore 
no nation should receive laws from a despotic gov- 
ernment,' we should be clearly exceeding the con- 
tents of our premises. The minor term, many 
nations, was undistributed in the minor premise," 
and must not, consequently, be used in a distributed 
sense in the conclusion. While it is comparatively 
easy to detect an illicit process of the minor, it is 
much more difficult as a rule to detect an illicit 
process of the major. The following from Creighton 
is an example of the latter fallacy. "All rational 
beings are responsible for their actions ; brutes are 
not rational beings; therefore, brutes are not re- 
sponsible for their actions." 



FALLACIES 537 

Fallacies of Insufficient Premises. These consti- 
tute the second class of categorical fallacies, and 
they may be described as breaches of those rules of 
the syllogism that were considered and illustrated 
above as rules of quality and rules of quantity. The 
rules of quality refer to the grounds on which affir- 
mative and negative conclusions can be based, and 
the rules of quantity to the grounds on which uni- 
versal and particular conclusions can be based. In 
the main, we apprehend that these rules have caused 
the student no great difficulty, and that he will have 
become familiar with their application. But because 
limiting instances are liable to cause more or less 
confusion, because, that is, we find it difficult to keep 
strictly within the boundaries within which any set 
of rules applies, we direct attention again to the fact 
that there are conditions which preclude certain 
propositional statements from rendering valid con- 
clusions. It is a general fact that conclusions do 
not follow from any combination of propositions. 
If we wish to support a conclusion by premises or 
grounds, those premises must have a character from 
which the conclusion can be shown to follow, and 
that means that a certain other character is strictly 
forbidden. Now, if this is true of particular con- 
clusions, we may go further and ask whether there 
are any combinations of propositions which support 
no conclusion whatever, that is, whether there are 
any limits of strictly categorical argumentation. 
Now such limits to all categorical inference we find 
in the two cases that are included here for con- 



538 A TEXT-BOOK OF LOGIC 

sideration, the cases, namely, of negative and par- 
ticular premises. We have shown above that any- 
attempted reasoning on the grounds of particular or 
negative premises involves us in one or other of the 
fallacies of distribution; but what is more impor- 
tant to remark now is that the study of these two 
cases enables us to insist upon certain character- 
istics of syllogistic reasoning which are fundamental 
to our understanding and employment of this type 
of argument. The syllogism, it should be observed, 
rests upon the possibility of making with respect 
to the subject-matter of the argument an affirmative 
and universal statement. The universal statement 
need not be affirmative, and the affirmative state- 
ment need not be universal ; but unless the premises 
contain the statement of universal affirmative rela- 
tions, no conclusion whatever can be drawn. Con- 
versely, if we wish to ground a belief on premises 
from which it can be shown to follow, these prem- 
ises, considered as a combination of propositions, 
must be universal and affirmative. Indeed, this is 
only to say that any categorical argument must con- 
form to the character of syllogistic reasoning. For, 
to speak of syllogistic reasoning at all, is to imply 
that conclusions are inferred from, or rest upon, 
statements about a given subject-matter which are 
affirmative and universal in the sense in which those 
terms have been explained. Now, if this is the true 
character of the syllogism, it follows that particular 
premises, whether they be both negative, or both 
affirmative, or one negative and the other affirm- 



FALLACIES 539 

ative, cannot express the structure of a syllogistic 
argument, because they do not contain the note of 
universality; and that negative premises also fail 
to do so, whether both premises are universal or 
only one is, since they fail to express the note of 
affirmation. To ground a conclusion upon premises 
which fulfil only one of the conditions of a cate- 
gorical argument, that is, upon propositions which 
are affirmative without being universal, or upon 
propositions which, although universal, are not 
affirmative, is to fall into one or the other of the 
fallacies of insufficient premises. In the former 
case, we have the fallacy of particular premises, 
and in the latter, the fallacy of negative premises. 

Hypothetical Fallacies may be defined as those 
mistakes in reasoning which render the conclusions 
of hypothetical arguments erroneous. Hypothetical 
arguments, as we have seen, derive their character 
from the relation of antecedence and consequence 
which is expressed in their major premise. Two 
observations only need to be made to remind our- 
selves of the nature and limits of hypothetical 
arguments. The first is that the major premises of 
such arguments are always hypothetical proposi- 
tions, that is, propositions which state a relation 
between two possibilities. From the fact that a 
relation of antecedence and consequence is always 
affirmed between these two possibilities in hypothet- 
ical propositions, it follows that the acceptance of a 
hypothetical statement commits us to the belief that 
the possibility which is expressed as the consequent 



540 A TEXT-BOOK OF LOGIC 

can be regarded as an actual fact, only when the 
possibility expressed as the antecedent states a con- 
dition which is known to be fulfilled. We cannot 
argue in the reverse order, that is, from the known 
existence of the consequent to the existence of the 
antecedent. The second remark is that the major 
premise affords no guarantee that the condition it 
states is anywhere fulfilled, and, consequently, no 
guarantee that the fact stated in the consequent is 
any where to be met with. Whether the antecedent 
or consequent is a fact that the minor premise can 
affirm or deny, depends upon whether either has 
been observed. Thus, the possibility of a hypothet- 
ical argument rests upon our ability to affirm or 
deny, for some other reason than the major premise 
itself affords, one or other of the possibilities be- 
tween which the major premise postulates a rela- 
tion; but within these limits the validity of such 
arguments depends upon a proper interpretation of 
the relation between antecedent and consequent as- 
serted by the major premise. It is, consequently, to 
a misunderstanding of this relation that we must 
look for the source of the fallacies which render the 
conclusions of hypothetical arguments erroneous. 

The hypothetical fallacies are due, as we said 
just now, to a wrong interpretation of the relation 
between antecedent and consequent asserted in a 
hypothetical proposition. Now, since there are two 
terms in a hypothetical proposition each of which 
we may affirm or deny, the relation between ante- 
cedent and consequent may be interpreted, theo- 



FALLACIES 541 

retically, in any one of four possible ways. It might 
be interpreted to mean that (1) if the antecedent 
is affirmed, the consequent may also be affirmed; 
(2) if the antecedent is denied, the consequent may 
also be denied; (3) if the consequent is affirmed, 
the antecedent may also be affirmed; (4) if the con- 
sequent is denied, the antecedent may also be denied. 
Now, as we pointed out before, it is only when the 
minor premise either affirms the antecedent or 
denies the consequent that the relation asserted in 
the major premise is interpreted correctly; only 
two, therefore, of the alternatives enumerated above 
represent truly the relations involved in a hypo- 
thetical proposition. When either of the other rela- 
tions is asserted in the minor premise of an argu- 
ment, that is, when the minor either affirms the con- 
sequent or denies the antecedent, the argument 
must be rejected as fallacious. The fallacy of deny- 
ing the antecedent leads to an eroneous denial of 
the consequent, and the fallacy of affirming the con- 
sequent leads to an erroneous affirmation of the 
antecedent. Both fallacies, as we shall see, arise 
from the neglect of an underlying material fact of 
considerable importance for a correct understanding 
of the hypothetical syllogism. 

In general, it may be remarked that the hypo- 
thetical fallacies are due, on the material side, to a 
failure to recognize the complexity and interconnec- 
tion of natural events. It is true that the object 
of our study of nature is to determine, in the strict 
sense, causal connections, that is, relations between 



542 A TEXT-BOOK OF LOGIC 

phenomena of such a nature that, not only does the 
consequent follow from the antecedent, but the 
stated antecedent is implied in the occurrence of 
the consequent. Our knowledge of natural events, 
however, frequently falls below this standard, and 
we have to be satisfied with the affirmation of a one- 
sided relation, that is, with the statement of a rela- 
tion between antecedent and consequent of such a 
nature that while the former is always followed by 
the latter, it does not always and necessarily pre- 
cede the latter. There are large areas of knowl- 
edge, in other words, in which the relations involved 
fail to display the characteristics of causal con- 
nections, and in reference to them we are bound 
to recognise what Mill called a plurality of causes. 
Now it seems to be the neglect of this consideration 
that is really at the foundation of the fallacies 
which befall hypothetical arguments. For, as Mel- 
lone states, "if we deny the antecedent, we cannot, 
therefore, deny the consequent, for the latter may 
be true for other reasons, and if we affirm the con- 
sequent, we cannot affirm the antecedent, for the 
consequent may result from other reasons." In 
either case, that is to say, we must recognise the 
possible existence of more connections between 
antecedent and consequent than the one which is 
made the subject of statement by the major 
premise, and this possibility places limitations 
upon the interpretation which we can give to 
hypothetical statements. It is true that, if the major 
premise states a causal connection between the 



FALLACIES 543 

antecedent and consequent, we may argue from 
the affirmation or denial of the former to the affir- 
mation or denial of the latter, and vice versa. In 
any other case, the possible operation of a plurality 
of causes must be allowed to determine the limits 
which we place upon hypothetical arguments. From 
this point of view, it seems quite clear that when 
we argue, "If a man's character is avaracious, he 
will refuse to give money for useful purposes; this 
man refuses to give money for useful purposes, 
therefore, this man's character is avaracious," the 
conclusion is erroneous, not merely because the 
minor premise affirms the consequent, but because, 
as we all know, there are other reasons, not at all 
connected with a man's character, which may make 
a refusal of the kind in question the necessary and 
right course for him to pursue, And it seems 
equally obvious that when we argue, 'If some agree- 
ment is not speedily arrived at between employers 
and workmen, the trade of the country will be 
ruined, an agreement will not be arrived at and 
therefore the trade of the country will be ruined,' 
the conclusion is erroneous, not merely because the 
antecedent is denied, but because the prosperity of 
a country depends upon other conditions than the 
one specified in the antecedent of the major premise. 
In both these instances we see that the breach of the 
formal rule of hypothetical arguments is tanta- 
mount, on the material side, to the neglect of the 
plurality of causes, that is, to the failure to recog- 



544 A TEXT-BOOK OF LOGIC 

nise the complexity and interconnection of natural 
events. 

Disjunctive Fallacies may be defined as those mis- 
takes in reasoning which render the conclusions of 
disjunctive arguments erroneous. Disjunctive argu- 
ments, as we have seen, derive their character from 
the fact that the major premises of such arguments 
state a series of alternative predicates any one or 
more of which, as a matter of fact, may be found 
to qualify their subjects. Any conclusion which is 
reached on the basis of a disjunctive major premise 
is valid or erroneous according as the enumerated 
alternatives do or do not conform to the conditions 
of disjunctive statements, and as the inference is 
or is not warranted by the premises on which it is 
made to rest. With respect to the nature of dis- 
junctive statements, it is sufficient to recall that 
these must satisfy three conditions. First, the 
alternatives must all fall within a single universe; 
not any set of terms that we can state in the form 
of 'either — or' are, in the logical sense, disjunctive. 
Second, the terms of the disjunction must be ex- 
haustive; all the species that fall within the uni- 
verse must be enumerated disjunctively. Third, we 
saw that the alternatives do not necessarily, although 
they sometimes do, exclude each other; it does not 
follow, therefore, that only one of the predicates 
can belong to the subject under the conditions that 
determine a particular argument. Whenever we 
fail to observe either one of these requirements of 
disjunctive statements in the process of argument, 



FALLACIES 545 

we are guilty of one or another of the disjunctive 
fallacies. 

The fallacy of false disjunction occurs when we 
proceed to a conclusion on the ground of a major 
premise in which the presented alternatives do not 
all belong to a single genus. The neglect of the first 
positive condition of disjunctive statements leads 
necessarily to fallacious arguments, because, where 
it is not satisfied, there is no common field within 
which the systematic connections of things, as set 
forth in disjunctive statements, may be said to fall. 
A failure to keep clearly before oneself the fact 
that disjunctive alternatives are definitely alter- 
natives within a single field of knowledge, reveals 
an entire misapprehension of the nature of disjunc- 
tive statements, and leads unavoidably, therefore, 
to erroneous conclusions. When, for example, we 
are prepared to find in a stranger to whom we have 
been introduced all sorts of social virtues merely on 
the ground that he has come from our home town, 
or when race prejudices make us blind to the vir- 
tues that individuals of a particular race display, 
we are, in all probability, guilty of the fallacy of 
false disjunction. The logical process underlying 
social attitudes of the kind in question may be illus- 
trated as follows : 'Either from my home town or 
devoid of all or certain current social virtues ; from 
my home town, therefore not devoid, etc/ 

The fallacy of incomplete disjunction occurs when 
we proceed to a conclusion on the ground of a major 

35 



546 A TEXT-BOOK OF LOGIC 

premise in which the presented alternatives are 
not exhaustively enumerated. It is true, of course, 
that the observation of single facts may lead to a 
disjunctive statement which does not meet the con- 
dition of complete enumeration. We may say, for 
example, 'This tree is an oak or an ash/ But prop- 
ositions of the kind just illustrated, while they may 
serve as minor premises of disjunctive arguments, 
cannot serve as major premises, for the reason that, 
although the universe within which the alternatives 
fall has been accurately determined, the alternatives 
within that universe have not been completely enu- 
merated. The necessity of a complete enumeration 
of the alternatives is due to the fact that the dis- 
junctive syllogism is intended to show, not only 
what a thing is, but also to determine, within the 
genus to which it belongs, what it is not. Let us 
suppose that a particular tree is either an oak or an 
ash. Then, if we argue, 'This tree is an oak or an 
ash, it is an oak, and therefore it is not an ash/ the 
argument would be formally valid, and the conclu- 
sion would be true ; but if we supposed that the con- 
clusion stated the whole truth about the subject, we 
should fall into error due to the incomplete disjunc- 
tion of the major premise. Or, to take another illus- 
tration, let us suppose that a particular ore is not 
either gold or copper. If, then, we were to argue, 
'This specimen of ore is either gold or silver or 
copper or antimony ; it is not either gold or copper, 
and therefore it is either silver or antimony/ we 
have fallen clearly into a conclusion which is not at 



FALLACIES 547 

all necessarily true, for the specimen in question 
might be none of those enumerated in the major 
premise. Such a conclusion is erroneous because all 
the species of the genus to which the particular 
specimen belongs were not enumerated. But, some 
one may say, we cannot always meet this require- 
ment of complete enumeration, and are we, there- 
fore, precluded from arguing validly to a disjunctive 
conclusion ? The answer is that we must express the 
indeterminate state of our knowledge about objects 
in a complete enumeration if we are to reach valid 
conclusions, and we may do this without necessarily 
possessing an exhaustive knowledge of the subject 
to which the argument refers. Thus, to state the 
above argument in a form from which a valid con- 
clusion may be drawn we may say, 'This specimen 
of ore is either gold or silver or copper or antimony 
or some other species,' a statement which does not 
claim complete knowledge of the subject-matter of 
the argument, but does rest upon a complete deter- 
mination of the knowledge that is possessed about it. 
The fallacy of ambiguous disjunction occurs when 
we proceed to a conclusion on the ground of a major 
premise in which the presented alternatives are not 
precisely determined with respect to their exclusion. 
We have seen that any proposition of the form *S is 
either AorB' strictly interpreted means *S is either 
A or else B,' but we also saw that the alternatives 
do not necessarily preclude the possibility that 'S 
may be both A and B.' Unless, therefore, we take 
special pains to make clear, in particular instances, 



548 A TEXT-BOOK OF LOGIC 

in which of these two ways the disjunctive major 
is to be interpreted, we are likely to be led to a con- 
clusion which leaves us in doubt as to the meaning 
of that conclusion. If we argue, for instance, that 
'Because all male students of the university either 
drill, or play football, or baseball or tennis, and be- 
cause X drills, therefore, he does not play football 
or baseball or tennis,' we are stating a conclusion 
of the individual which may be true, but it is not 
true for the reason assigned; for there is nothing 
in the universe of physical education as conducted 
by the university that makes an exclusive interpret 
tation of the enumerated alternatives necessary. If, 
then, we give an exclusive interpretation to a non- 
exclusive series of alternatives, or a non-exclusive 
interpretation to an exclusive series, we are guilty 
of the fallacy of ambiguous disjunction. 

REFERENCES 

SEE THE END OF THE NEXT CHAPTER 

QUESTIONS 

1. What is the name and character of Aristotle's treatise 
on fallacies? 

2. In what senses is the term fallacy used at the present 
time? 

3. In what two main groups did Aristotle classify the fal- 
lacies? 

4. To what distinctions drawn in the text do Aristotle's 
main groups correspond? 

5. Describe the chief features of each of the four main 
classes into which the text divides fallacies, and by what 
names are they distinguished? 



FALLACIES 549 

6. Into what subdivisions, and according to what prin- 
ciple, may the fallacies of interpretation be divided? 

7. What do understand by verbal ambiguity, and how does 
it differ from mere indetterminateness in the meaning 
of words? 

8. Describe and illustrate the fallacy of equivocation. 

9/ What is the fallacy of accent, and in what respect does 
the corresponding Greek fallacy differ from it? 

10. In what several ways may one fall into a fallacy of 
accent? Illustrate. 

11. Describe and illustrate the fallacies of composition and 
division. 

12. What is the Latin name for the fallacy of accident? 
Illustrate the fallacy. 

13. Give an illustration of the converse fallacy of accident, 
and by what Latin name is it known? 

14. Describe the character of structural ambiguity. 

15. What is the fallacy of amphibole, and from what other 
kinds of ambiguity must it be distinguished? 

16. State and illustrate the fallacy of false parenthesis. 

17. What do you understand by fallacies of implication, 
and into what two classes may they be divided? 

18. What is a fallacy of opposition? 

19. To what fallacies are the following logical relations 
particularly liable: contrariety, subcontrariety, subal- 
ternations? 

20. What is a fallacy of education? 

21. State what is meant by a fallacy of obversion. 

22. What is a fallacy of conversion, and in respect of what 
propositions, and why, is it likely to occur? 

23. What are fallacies of inference, and into what two 
classes may they be divided? 

24. What is a deductive fallacy, and how are such fallacies 
classified? 

25. What is a categorical fallacy? 

26. What is meant by a fallacy of four terms, and state in 
what two ways such fallacies arise 



550 A TEXT-BOOK OF LOGIC 

27. Classify and describe each of the fallacies of four terms. 

28. What are fallacies of insufficient premises, and what 
rules of the syllogism do they break? 

29. Show, in relation to the nature of syllogistic reasoning, 
how the fallacies of particular and of negative premises 
occur. 

30. Describe as fully as you can the character of an hypo- 
thetical fallacy. 

31. State and illustrate the two hypothetical fallacies. 

32. How does the fact that natural events are complex 
affect our interpretation of hypothetical statements? 

33. What do you understand by a disjunctive fallacy? 

34. Into what classes, and according to what principle, may 
disjunctive fallacies be divided? 

35. State and illustrate the fallacy of false disjunction. 

36. Describe the fallacy of incomplete disjunction. Illus- 
trate. 

37. What is the fallacy of ambiguous disjunction? Illus- 
trate. 

EXERCISES 

Examine the following arguments and state in what respect, 
if any, they are fallacious, the technical name of the 
fallacy of which each is guilty, and the class to which 
the fallacy belongs: 

(1) It is sometimes argued that the communication of 
an infectious disease to another person should be 
punished by law, since the law exists for the pur- 
pose of protecting people from harm. 

(2) I have made thee free a slave. 

(3) How can you argue that it is wrong for me to 
assist my friend to obtain the office by offering 
business or financial considerations to the voters 
of my acquaintance if you agree that it is right 
for a man to do what he can for his friend's good? 

(4) A commercial traveller wrote to his chief: Dear 
Sir, On Wednesday next I want you to allow me 



FALLACIES 551 

the day off. My wife having lost her mother is 
being buried on that date and I should like to at- 
tend the funeral. 

(5) A, B, C, are all the known instances of the class 
X, and since they are all found to possess the 
characteristic p we may conclude that All X is p. 

(6) Large numbers, though not all, of the instances 
of the class X have invariably been found to ex- 
hibit the character p, therefore, All X is p. 

(7) If it is false that no men are immortal, it must 
certainly be true that all men are mortal, since 
there is no middle position between mortal and im- 
mortal. 

(8) If you perform an unfriendly act, I may certainly 
conclude that your attitude is hostile. 

(9) He who is content with what he has is truly rich, 
but the covetous man is not content with what he 
has, no covetous man, therefore, is truly rich. 

(10) All Parisians are Frenchmen indeed, when the only 
reason you have to advance for that statement is 
that all Parisians and all Frenchmen are Euro- 
peans ! 

(11) What is not compound is an element, gold is not 
compound, and is, therefore, not an element. 

(12) If a substance is a metal, it is a good conductor 
of heat and electricity, but this substance does not 
conduct either well, and so it cannot be a metal. 

(13) If man were not capable of progress, he would 
not differ from the brutes, but since he does differ 
he must be regarded as capable of progress. 

(14) What you speak of must be either blue or green 
or yellow, but since you say that it is neither of 
these it must be devoid of colour. 

(15) That happened on Monday or Thursday or in April, 
but it was not in April for I remember that it was 
Harvest; it must, therefore, have happened on 
Monday or Thursday. 



CHAPTER XIX 

FALLACIES (CONTINUED) 

Inductive Fallacies. By fallacies of induction, 
as was stated above, we understand those errors to 
which thought is exposed in its endeavour to deter- 
mine the principle of connection between a number 
of particular facts. Now, since induction requires 
as a condition of the explanation of the particulars 
of experience, that the facts of experience be care- 
fully observed, it is obvious that we are exposed 
mainly to two classes of inductive error, to those, 
namely, which arise in connection with our obser- 
vation of facts, and to those which arise in connec- 
tion with our explanation of facts. But since lan- 
guage is an indispensible instrument both for record- 
ing what we observe, and for stating the methods 
and results of the explanations that we have to offer 
of what is observed, we may include in the present 
discussion a brief statement of the nature and 
sources of the fallacies into which a careless use of 
language may be the means of leading us. The fal- 
lacies of induction will, then, be studied under three 
heads ; first, those which originate in our use of lan- 
guage; second, those which involve errors of obser- 
vation; and third, those which occur in connection 
with the so-called inductive inference, the errors, 
that is to say, which invalidate explanation. 

(552) 



FALLACIES 553 

Fallacies of Language. Readers of Plato cannot 
fail to have remarked that the difficulties that he 
sometimes experienced in making clear to himself 
and to others the character of some of the more 
elementary logical distinctions was due, in great 
measure, to the fact that the nature of even simple 
grammatical distinctions was not clearly under- 
stood by him and his contemporaries. The fact 
that Aristotle attributed, as we have seen, a large 
number of the fallacies to the influence of language, 
also points to the close connection that there is 
between thought and human speech. In more mod- 
ern times, Bacon, Hobbes, Locke, and others, have 
remarked upon the dangers to which we are liable 
through the words that we employ to express our 
ideas, and Mill wrote two chapters in which he 
discusses the requirements and principles of what 
he calls a "philosophical language." These refer- 
ences, which might be indefinitely extended, are 
enough to show that while our acquired speech 
may be sufficient for the ordinary purposes of life, 
it must be carefully employed if, in regard to the 
subjects of scientific investigation, it is not to become 
a source of embarrassment and error. 

Bacon gave the name of Idols of the Market- y 
Place (Idola fori) to the fallacies which were due 
to language, and he puts the sum of the matter as 
follows: "Men imagine that their reason governs 
words whilst, in fact, words react upon the under- 
standing; and this has rendered philosophy and the 
sciences sophistical and inactive." The same truth 



554 A TEXT-BOOK OF LOGIC 

is dwelt upon at length by Locke, and the general 
nature of the influence that language is capable of 
exerting prejudicially upon thought, the only point 
with which we are here concerned, is evident from 
the following quotation: "Men," he says, "having 
been accustomed from their cradles to learn words 
which are easily got and retained, before they knew 
or had framed the complex ideas to which they were 
annexed, or which were to be found in the things 
they were thought to stand for, they usually con- 
tinue to do so all their lives; and, without taking 
the pains necessary to settle in their minds deter- 
mined ideas, they use their words for such unsteady 
and confused notions as they have, contenting them- 
selves with the same words other people use, as if 
their very sound necessarily carried with it con- 
stantly the same meaning. . . . This inconsistency 
in men's words when they come to reason concerning 
either their tenets or interest, manifestly fills their 
discourse with abundance of empty, unintelligible 
noise and jargon, especially in moral matters, where 
words, for the most part, standing for arbitrary 
and numerous collections of ideas not regularly and 
permanently united in nature, their bare sounds are 
often only thought on, or at least very obscure and 
uncertain notions annexed to them. Men take the 
words they find in use amongst their neighbours; 
and, that they may not seem ignorant what they 
stand for, use them confidently, without much 
troubling their heads about a certain fixed meaning ; 
whereby, besides the ease of it, they obtain this 



FALLACIES 555 

advantage: That, as in such discourses they seldom 
are in the right, so they are as seldom to be con- 
vinced that they are in the wrong; it being all one 
to go about to draw those men out in their mistakes 
who have no settled notions, as to dispossess a 
vagrant of his habitation who has no settled abode." 
Fallacies of Observation. Observation may be 
defective chiefly in two respects. It may be insuffi- 
cient in amount, or incomplete or imperfect in 
detail. If we consider these two cases separately, it 
must not be forgotten that, frequently and perhaps 
usually, the fallacies which depend upon observation 
occur as the result of both kinds of defect. Induc- 
tion, as we have seen, depends upon the collection 
of data sufficient in amount to suggest a law of con- 
nection; but, more important than the number of 
the facts observed, is the degree of thoroughness 
with which we are able to analyse them. Mere col- 
lections of fact, if such a thing were possible, have, 
as we have seen, no special value for science, and 
alone can lead to the formulation of no general 
principles of connection. The particular data which 
are the material of science are brought under obser- 
vation by the exercise of discrimination, comparison, 
synthesis, in a word, judgment; and this differs 
in no essential respects from the process by which 
we detect, within collected groups of fact, the fea- 
tures that are common, and the connections that 
are causal. But while this should be kept clearly in 
mind, it is nevertheless true that we may be led into 
an inductive fallacy, either because the amount of 



556 A TEXT-BOOK OF LOGIC 

data available does not warrant an inference, or 
because, although sufficient in amount, our analysis 
of the data has not been carried out with sufficient 
care and thoroughness. 

Observation, then, is defective, in the first place, 
when the number of the observed data is not suffi- 
cient in amount to guarantee the conclusion that is 
based upon it. In view of the situations which this 
statement has in view, we are particularly inter- 
ested, in logic, to ascertain what are the conditions 
that lead to insufficient observation. One important 
condition is the general tendency to neglect the 
observation and collection of what are called nega- 
tive instances. By a negative instance is meant an 
instance in which a given phenomenon is observed 
not to occur. If we take, for example, the popular 
superstitions, — such, for instance, that it is un- 
lucky to begin any new task or undertake any new 
enterprise on Friday, for people to be associated 
together in groups of thirteen, or to walk under a 
ladder that is inclined against a wall, — we are 
seriously expected, by those who entertain them, to 
share these superstitions in view of the instances 
that these persons are able to enumerate in which 
some untoward result has occurred. An enumer- 
ation of the instances in which no such consequence 
has followed, it would seem, is sufficient to show that 
the superstitituous conclusion is defective if not 
fallacious by reason of the failure to observe these 
negative instances. 



FALLACIES 557 

To have called our attention to this tendency to 
neglect the evidence afforded by negative instances 
is one of the merits of Bacon. The following quo- 
tation from the Novum Organum, not only states 
the nature of the fallacy, but indicates also its scope. 
Bacon writes: 'The human understanding, when 
any proposition has been once laid down (either 
from general admission and belief or from the 
pleasure it affords), forces everything else to add 
fresh support and confirmation; and although most 
cogent and abundant instances may exist to the con- 
trary, yet either does riot observe or despises them, 
or gets rid of and rejects them by some distinction, 
with violent and injurious prejudice, rather than 
sacrifice the authority of its first conclusions. It 
was well answered by him who was shown in a 
temple the votive tablets suspended by such as had 
escaped the peril of shipwreck, and was pressed as 
to whether he would then recognise the power of 
the gods : But where are the portraits of those who 
have perished in spite of their vows? All super- 
stition is much the same, whether it be that of 
astrology, dreams, omens, retributive judgment, or 
the like, in all of which the deluded observers 
observe events which are fulfilled, but neglect and 
pass over their failure, though it be much more 
common. But this evil insinuates itself still more 
craftily in philosophy and the sciences, in which a 
settled maxim vitiates and governs every other cir- 
cumstance, though the latter be much more worthy 
of confidence. Besides, even in the absence of that 



558 A TEXT-BOOK OF LOGIC 

eagerness and want of thought (which we have 
mentioned), it is the peculiar and perpetual error 
of the human understanding to be more moved and 
excited by affirmatives than by negatives, whereas 
it ought duly and regularly to be impartial ; nay, in 
establishing any true axiom the negative instance 
is the more powerful." 

The testimony of Darwin is to the same effect. 
He says : "The success of the 'Origin' may, I think, 
be attributed in large part to my having long before 
written two condensed sketches, and to my having 
abstracted a much larger manuscript, which was 
itself an abstract. By this means I was enabled to 
select the more striking facts and conclusions. I 
had also, during many years, followed a golden rule 
— namely, whenever a published fact, a new obser- 
vation or thought, came across me, which was op- 
posed to my general results, to make a memorandum 
of it without fail and at once; for I had found by 
experience that such facts and thoughts were far 
more apt to escape from memory than favourable 
ones. Owing to this habit, very few objections were 
raised against my views which I had not at least 
noticed and attempted to answer." 

Another condition of insufficient observation 
that may be mentioned is education. Whatever our 
conception of the aim of education may be, there is 
no doubt that a large part of the educative process, 
as we actually experience it, is taken up with an 
effort to gain familiarity with a body of knowledge 
that is regarded as traditionally important and fun- 



FALLACIES 559 

mental. This statement is true for all grades of 
education from the grammar school to the univer- 
sity. Now it is not only inconceivable, but contrary 
to experience, that the acquisition of any con- 
erable body of knowledge should be without its 
effect upon our mental habits; for acquaintance 
with any class of facts means, in terms of men- 
tal habit, a trained ability to perceive with in- 
creasing facility other facts that are the same in 
kind as these, and a corresponding inability to per- 
ceive facts that differ considerably from them in 
kind. A particular illustration of this general truth 
is found in the case of those individuals whose edu- 
cation assumes a special character, as it does, for 
instance, in law, medicine, theology, engineering, 
etc. And even if we consider the case of those 
whose common school education is not followed by 
a university training, but by apprenticeship in some 
business, it is quite apparent, even then, that the 
knowledge of the business, of its material, methods, 
and aims, acts exactly in the same way to sharpen 
the perception to observe a specialised group of 
facts, and to limit the facility with which facts 
dissimilar to these are perceived. The truth is 
that all of us perceive what we are educated to 
perceive, and that we are limited in respect to the 
kinds of things that we perceive by the education 
that we have received. 

Bacon referred to the errors into which we are 
led as the result of the limitations that education 
and inherited beliefs may have upon the range of 



560 A TEXT-BOOK OF LOGIC 

J our perceptions as Idols of the Theatre (Idola The- 
atri). Doubtless, as is shown by his illustrations, 
he had in mind the cramping effect of the traditions 
of the Schoolmen upon the new learning in his day. 
Bacon lived at the dawn of the modern scientific 
era, and he was acquainted with some of the ob- 
stacles that it had to encounter on account of theo- 
logical prejudice (odium theologicum) of the times. 
But if we have passed beyond the stage where the 
prejudices which come from a one-sided theological 
position and training are allowed to interfere with 
the freedom of thought and investigation, it is still 
possible that prejudices the same in kind, though 
different in form, may hamper the human mind in 
its search for truth. The fact that these hindrances 
are not officially administered, but are grounded in 
that specialisation, upon which our modern educa- 
tion lays so much importance, would make the ten- 
dency to which we are referring the more insidious, 
and hence more difficult to detect and avoid or over- 
come. "The success of modern scientific methods," 
as Creighton remarks, "has sometimes led investi- 
gators to despise and belittle the work of those who 
do not carry on their investigations in laboratories, 
or do not weigh and measure everything." Thus 
the mechanical conceptions which were worked out 
successfully in the realm of physics and astronomy, 
have been extended to psychology, ethics, and polit- 
ical science, without any consideration being given 
to the differences in the material which is the sub- 
ject-matter of this latter group of sciences. In our 



FALLACIES 561 

own day, the evolutionary hypothesis has provided 
us with a point of view for looking at all the details 
of human experience; but it is not impossible that 
the limitations of this point of view and the errors of 
observation to which it has led, may, at some future 
time, be as clear as today are the insufficiencies of 
the notion of mechanism as employed by the thinkers 
of the eighteenth century. 

In the second place, observation may be defective 
either because it is incomplete or imperfect in detail. 
The instances of fallacious inference which belong 
in this group are those which arise from the fact 
that the collected data, upon which the inferences 
rest, have not been examined with sufficient thor- 
oughness. Defects of the kind here in question may 
be due either to the fact that only part of the mate- 
rial has been studied, or to the fact that, while all 
the material may have been studied, this has not 
been done for all or parts of the material with suffi- 
cient minuteness. In either case, the inference will 
be erroneous on account of a failure to carry our 
analysis of the phenomenon under observation into 
sufficient detail. 

A number of conditions may operate to arrest 
our analysis of observed data at a point which falls 
short of that at which it is possible to determine 
with some degree of accuracy the law of their 
connection, but two are, from the logical point 
of view, of sufficient interest to require brief men- 
tion. There is no doubt, in the first place, that great 

36 



562 A TEXT-BOOK OF LOGIC 

differences exist in the ability of different investi- 
gators to perform the task of analysing a group of 
collected facts. Some individuals, it is found, are 
splendid collectors, and are exceedingly fertile in 
devising ways and means of bringing under obser- 
vation specimens that entirely escape the notice of 
others not gifted as themselves. But it sometimes 
happens that among these born collectors there are 
many who can go but a little way toward that com- 
plete analysis of their collected material upon which 
alone any general conclusion can safely be based. 
The recognition of this fact has led, in practice, to 
the introduction of a large amount of cooperation 
between workers in the same line of research, and 
has tended to make the laboratory a workship in 
which there is found employment for a great variety 
of talent. It is only the exceptional man who, like 
Darwin, combines the collector's skill with a keen 
analytic mind that brings to light the common fea- 
tures that lie hidden under a mass of differences in 
any group of facts. Natural limitations, then, of 
the sort we are discussing operate frequently to 
render the observation of details incomplete, and to 
throw doubt upon any conclusion which rests upon 
such imperfectly analysed data. 

Another condition which tends to make analysis 
defective is an imperfectly developed technique or 
method. We have spoken above of the importance 
of the construction and use of apparatus if the work 
of scientific observation is to be successfully carried 
on. Indeed, we may say that the progress of modern 



FALLACIES 563 

science has been dependent, in large measure, on 
the success that has attended the development of 
special methods for bringing the structure of col- 
lected data under detailed observation. In the bio- 
logical sciences, for example, the methods of hard- 
ening, embedding, and staining the various tissues 
have gone a long way toward placing these sciences 
on the same experimental plane as physics and 
chemistry. The further progress of these, as of the 
other, sciences depends upon the adaptation of the 
methods already in vogue to new material, and the 
development of new methods to meet new conditions 
and situations as they arise. But whenever we 
speak of improvement, and recognise the possibility 
of new discoveries, we at the same time imply that 
our present knowledge is defective in just those 
respects in which advancement may be expected. 
This, however, is only to say that so long as the 
technique of any science is capable of improvement, 
the conclusions of that science must be entertained 
with caution and subject to certain reservations. 

Fallacies of Explanation. There are two sources 
of error in inductive processes of reasoning to which 
we shall direct attention: hasty generalisation and 
false analogy. It is exceedingly difficult to give a 
concise statement of what is meant by hasty general- 
isations, since any explanation may be rendered 
erroneous by undue haste at any of the stages of the 
inductive process. For instance, an inductive con- 
clusion may be fallacious on account of haste at 
either the stage of what was called above empirical 



564 A TEXT-BOOK OF LOGIC 

generalisation, or at the stage of hypothesis, or at 
the stage of verification. Whenever, therefore, any 
part of the task of explanation is not thoroughly 
performed, our conclusion, resting as it does upon 
an incomplete or imperfect acquaintance with the 
details of the phenomenon, may be called a hasty 
or premature generalisation. The essential nature 
of the fallacy consists, then, in the absence of an 
analytic thoroughness requisite for a true explana- 
tion, without respect to the part of the explanatory 
process in which the failure to be sufficiently thor- 
ougs occurs. 

We may remark, however, that we are not guilty 
of this fallacy when we consciously arrest our anal- 
ysis of a phenomenon to be explained at a point 
which falls short of completeness, or when imper- 
fectly observed or analysed data are generalised, 
but are not offered as an explanation. The fallacy 
occurs only when an incomplete analysis is presumed 
to be complete, or when a preliminary generalisation 
is mistaken for a final one. As has been said, the 
value of logic consists in calling attention to the fact 
that, not only must conclusions be true, but the 
reasons for the truth of conclusions must be defi- 
nitely ascertained, if science is to exist. Science, as 
we have seen, is a consciously controlled process, a 
process of arriving at a certain conclusion, by means 
of a method which is definitely regulated at all the 
stages through which it passes from the earliest 
observation to the finally accepted explanation. 
When the control of the method by which conclu- 



FALLACIES 565 

sions are reached gets out of hand, when we become 
careless in the use of the methods we adopt for the 
examination of phenomena, our explanation of such 
phenomena is erroneous, because it involves, in the 
sense in which the term has been explained, a hasty 
generalisation. Such conclusions are fallacious be- 
cause they do not rest upon a sufficiently detailed 
basis of fact. 

Analogy may give rise to erroneous conclusions 
when it is supposed that the phenomenon under 
observation has all the characteristics of the instance 
which provides us with the analogical resemblance. 
We have seen that analogy is a useful method, or 
step in the method, of scientific explanation, but 
unless it is strictly guarded it is likely to arouse all 
sorts of distracting associations which lead to mis- 
understanding and error. When considered as a 
possible source of error, analogy has certain affin- 
ities with figurative language, on the one hand, and 
with the disregard of negative instances, on the 
other. With respect to its relation to figurative 
language, analogy leads us astray when the illustra- 
tion which provides us with the analogical resem- 
blance engages the whole attention, and we are 
thereby led to predicate of the phenomenon under 
investigation qualities that have been actually ob- 
served only in the illustration. It was with the dan- 
gers of analogical reasoning in mind that a professor 
was wont to say to his students that they should 
not try to make the parables of the New Testament 
"go on all fours," that is, they must not try to find 



566 A TEXT-BOOK OF LOGIC 

a point for point resemblance between the truth of 
the parable and the story which provided the basis 
of the analogy. It is neglect of such counsel that 
leads in the sciences to the fallacy of false analogy. 
With respect to its relation to negative instances, 
analogy is likely to lead us into error if the points 
of difference between a phenomenon and its illus- 
tration are lost sight of, and only the resemblances 
are retained. "For instance," to borrow an illus- 
tration from Sidgwick, "during the recent Boer 
War various analogies were appealed to by various 
people as helping to throw light on the situation. 
It was compared to the operations of America in 
the Philippines, to the Armenian massacres, to the 
American Civil War, and even to the high-handed 
action of Spain in the Netherlands in the time of 
Elizabeth. Our action in South Africa was sup- 
posed (by different people) to be analogous to those 
and other historical precedents, and the analogies 
were used to support the various judgments passed 
by these various people on the rights of the war and 
its probable outcome. It is easy to see that in all 
these comparisons there is some likeness and also 
some difference, and that the justice of the analogy 
depends upon the relevance of the likeness and the 
difference." But if the difference is a relatively 
important one, and we proceed nevertheless to build 
up an explanation on the ground of the likeness 
alone, we are guilty of the fallacy of false analogy. 
The fallacy assumes the converse form if we are led 
to underestimate the value of a resemblance because 



FALLACIES 567 

it is accompanied by striking differences. In any 
case, the fallacy arises when we forget that analog- 
ical reasoning depends upon what Sidgwick calls 
"the relevance of the likeness and difference." 

Fallacies of the Context. The fallacies that we 
have considered in the foregoing pages arise out of 
a failure to determine precisely the nature and rela- 
tions of the subject-matter which constitutes the 
contents of particular arguments. The group of 
fallacies to which we have now to direct attention 
arises from the fact that the meaning of particular 
arguments, as we have shown, is determined in part 
by their relation to a context which they imply with 
varying degrees of clearness. Now when we say 
that the context supplies part of the meaning that 
an argument may rightly be said to have, it is im- 
portant to bear in mind that the context may be 
said to refer, not only to the undetermined aspects 
of the subject-matter under discussion, but also to 
the interests or purposes which sustain, as we have 
seen, our inquiries into truth and our search for 
knowledge. Any discussion of what knowledge or 
truth is cannot fail to be inadequate, as we have 
shown, if attention is not given to the part played 
by the complex character of the material about 
which knowledge is desired, and also to the character 
of the interest which knowledge is intended to sat- 
isfy. Because, therefore, of its relation to a context, 
every argument is liable to errors which do not arise 
directly out of the facts and relations which are 
expressed by its constituent propositions. There 



568 A TEXT-BOOK OF LOGIC 

may be imported, that is to say, into the meaning 
of arguments elements from their contexts which 
lead to conclusions which are at variance with what 
the premises, logically interpreted, really support. 
Whenever this happens, whenever, that is, we accept 
arguments on the ground of suggestions, derived 
from their contexts, which are not related to the 
truth character of the arguments themselves, there 
ensues a fallacy of the context. A fallacy of the 
context may be defined, therefore, as an error in 
reasoning which is due to the influence that some 
feature or features of a context, not related to the 
truth character of the argument, has upon our inter- 
pretation of the subject-matter of the argument, 
such influence inducing us to accept a statement 
about the subject-matter of the argument as true for 
reasons which, apart from the influence referred to, 
would fail wholly or in part, to justify its accept- 
ance. 

The nature of these fallacies may be made still 
clearer, if we observe that in arguments of the kind 
under consideration the context may contribute 
irrelevant elements derived from either of the fac- 
tors by which, as was pointed out, human knowledge 
is determined, — from the world of relatively inde- 
pendent objects on the one hand, and from the world 
of our interests, on the other. An imperfect deter- 
mination of the universe within which an argument 
is intended to be considered leads to a group of fal- 
lacies of which Petitio Principii, Ignoratio Elenchi, 
Non Sequitur, and Complex Question are the chief; 



FALLACIES 569 

and a failure to confine the interests by which we 
are guided in our search for truth to those which 
have a direct relation to that end leads to another 
group of which Post Hoc, Argumenta ad Hominen, 
ad Populum, ad Vereeundiam, ad Misericordiam, 
may be taken as the most important. In the former 
group, we are considering how the relations which 
a given object has to other objects may become a 
source of error in our knowledge of the world of 
relatively objective things, and to these we may give 
the name, fallacies of assumption. In the latter, we 
are studying the ways in which knowledge may be 
deflected by reason of the operation of certain nat- 
ural and acquired characteristics of the mental life ; 
and to these we may give the name, fallacies of 
interest. In both cases the fallacy is due to the 
admission into our reasoning of elements which have 
no direct bearing upon the truth character of the 
judgments in which our knowledge is asserted. 

Fallacies of Assumption are those errors in rea- 
soning which occur when the assumptions on which 
an argument rests are not clearly distinguished from 
the judgments of which the argument consists. An 
assumption, in this connection, is anything we take 
for granted, but do not assert, about the subject- 
matter of an argument. It is the equivalent of what 
we have had occasion hitherto to speak of as the 
universe of discourse. Interpreted from this point 
of view, it is readily seen that an assumption is not 
an assertion, and forms no part of the asserted con- 
tents of an argument, although, as we have seen, it 



570 A TEXT-BOOK OF LOGIC 

has a relation to the argument, a relation which is 
indicated with sufficient clearness by saying that it 
points out the sphere of reference in which what is 
asserted may or not be accepted. Now it is a misin- 
terpretation of the relation between what an argu- 
ment assumes and what it asserts that lies at the 
foundation of the fallacies that we have here to con- 
sider. Thus, when what is taken for granted or as- 
sumed is allowed to function in any part of an argu- 
ment as an assertion or judgment, or when the as- 
sumption on which an argument proceeds is ambig- 
uous, the resulting fallacy is one of assumption. 

Petitio Princpii is the name of an argument which 
assumes the conclusion that is to be proved. It is, 
as Sidgwick says, "the surreptitious assumption of 
a truth you are pretending to prove." Since, then, 
the fallacy is one of assumption, it is evident that 
its source must be found, not in what is definitely 
asserted, but in the world of reality or existence in 
which what is asserted has a definite meaning or 
fulfillment, that is to say, in the universe of dis- 
course from the standpoint of which the argument 
is interpreted. The nature of the fallacy is seen in 
the confusion that exists, for the person guilty of 
it, between the asserted grounds of a conclusion, 
and the assumptions that thought postulates with 
respect to the subject-matter of an argument, 
Whenever it exists, the fallacy directs attention to 
the fact that the truth of what an argument asserts 
depends in part upon what assumptions the argu- 
ment makes ; and, in view of the nature of an argu- 



FALLACIES 571 

ment, it follows that when assumptions are put 
forward as reasons we necessarily fail to establish 
a conclusion, and fall into the merest dogmatism 
unless we are willing to have these assumptions 
called into question. "When," for instance, "Galileo 
maintained that the earth goes round the sun, he 
fully believed it and yet was willing to treat it as a 
disputable question ; but when Pope Urban VIII and 
his cardinals maintained that the earth stood still, 
they shut their eyes to the arguments, and said their 
view was only disputable by any one who chose to 
be burnt alive." Now, with respect to the right to 
call into question any of the grounds on which con- 
clusions are supposed to rest, we can only say that 
this right must be conceded, or that the fallacy we 
are now considering can have no logical standing. 
But further, if we cannot go behind the premises, 
nor consider the rights of assertions to stand as 
premises, but must accept any set of assertions at 
their face value as grounds of argument, then the 
whole of logic has been reduced to a mere formal 
science, and its processes are valuable only as they 
enable us to secure consistency of statement. Either 
this, or we must admit that there is a real difference 
between assertions and assumptions, between judg- 
ments and postulates, that the human mind is likely 
at times to fail to keep the distinction clearly before 
it, and, consequently, that the one may sometimes 
slip, in the course of argument, into the place of the 
other. Now, when this happens, when in the course 
of argument assumptions take the place of reasoned 



572 A TEXT-BOOK OF LOGIC 

judgments, the argument is fallacious because, for 
the reason assigned, it involves a petitio principii. 

The English language, as Whately pointed out, 
is peculiarly "suitable for the fallacy of Petitio 
Principii, from its being formed from two distinct 
languages, and thus abounding in synonymous ex- 
pressions which have no resemblance in sound, and 
no connection in etymology, so that a Sophist may 
bring forth a proposition expressed in words of 
Saxon origin, and give as a reason for it the very 
same proposition stated in words of Norman origin ; 
e. g. 'To allow every man an unbounded freedom of 
speech must always be, on the whole, advantageous 
to the State ; for it is highly conducive to the inter- 
ests of the community, that each individual should 
enjoy a liberty perfectly unlimited of expressing 
his sentiments.' " 

When the fallacy of petitio principii is com- 
mitted in a Single Step it is Called vcrrepov -rrporepav 

(hysteron proteron) ; and when it involves more 
than a single step it is called circulus in probando or 
reasoning in a circle. 

Closely connected with the foregoing is the fal- 
lacy of the Complex Question. By a complex ques- 
tion, in the broadest meaning of that term, is meant 
one that suggests its own answer. Any question, 
for instance, that forces us to select, and assert in 
our answer to it, one of the elements of the question 
itself, while some other possibility is really open, is 
complex in the sense in which that term is here em- 
ployed. If, for example, one were to ask whether 



FALLACIES 573 

you were going to New York or London, or if your 
favourite colour were red or blue, or if you had 
given up a particular bad habit, he would be guilty 
of the fallacy of the complex question, if, in each 
case, the alternatives, as a matter of fact, were more 
numerous than, or were in any way different from, 
those stated in the question. Any leading question 
which complicates an issue by over simplification is 
fallacious for the same reason. Now, in the light 
of what we have said with respect to the petitio 
principii, it is not difficult to see that the fallacy of 
the complex question is occasioned by the character 
of the assumption on which the question rests. In 
the petitio principii an assumption with respect to 
the subject-matter of an argument functions as a 
premise, in the complex question it is a similar as- 
sumption that shuts out some of the material possi- 
bilities of a situation and confines an issue within 
too narrow limits. As in the former case, so here, 
the only way of meeting the difficulty is to raise the 
previous question, that is, to call the assumption 
which lies back of the fallacy into question. 

Ignoratio Elenchi, according to Aristotle, is a 
fallacy which arises from "ignorance of the nature 
of refutation." In order to refute an assertion, 
Aristotle says we must prove its contradictory; the 
proof, consequently, of a proposition which stood in 
any other relation than that to the original, would 
be an ignoratio elenchi. 

Since Aristotle, the scope of the fallacy has been 
extended to include all cases of proving the wrong 



574 A TEXT-BOOK OF LOGIC 

point. Thus, when H. Spencer, in arguing against 
the advocates of a classical education, says that 
"Throughout his after career, a boy, in nine cases 
out of ten, applies his Latin and Greek to no prac- 
tical purposes," he is guilty of an ignoratio elenchi, 
for the argument, as Welton points out, "ignores 
the fact that the advocates of a classical education 
do not claim that Latin and Greek are of direct use 
in practical life. What they do urge is that the 
study of the classics furnishes an unrivalled mental 
training; and it is this proposition which a true 
eAeyxo? (elenchus) must disprove." With this inter- 
pretation of the fallacy Whately is in agreement. 
He writes : "I am required to prove a certain con- 
clusion ; I prove, not that, but one which is likely to 
be mistaken for it ; in that lies the fallacy. . . For 
instance, instead of proving that 'this person has 
committed an atrocious fraud/ you prove that 'this 
fraud he is accused of is atrocious / instead of prov- 
ing, as in the well-known tale of Cyrus and the two 
coats, that 'the taller boy had a right to force the 
other boy to exchange coats with him/ you prove 
that 'the exchange would have been advantag- 
eous to both/ instead of proving that 'a man 
has not a right to educate his children or dis- 
pose of his property in the way he thinks best/ you 
prove that 'the way in which he educates his chil- 
dren or disposes of his property is not really the 
best;' instead of proving that 'the poor ought to be 
relieved in this way/ you prove that 'they ought to 
be relieved.' " The fallacy usually occurs, as Jevons 



FALLACIES 575 

remarks, "in the course of long harangues, when 
the multitude of words and figures leaves room for 
confusion and forgetfulness." Hence, an ignoratio 
elenchi has been called by Aikins the fallacy of the 
forgotten issue. Thus it is frequently necessary, 
for example in debate, to call the discussion back to 
the point at issue. For example, in a speech in the 
House of Commons, Canning is reported to have 
said, in reply to Mr. Percival, that "The question is 
not, as assumed by my opponent, whether we shall 
continue the war in the Peninsula, but whether it is 
essential to our success in the war that our present 
system of currency remain unchanged/ ' 

The nature of the fallacy, then, consists in sub- 
stituting for a certain issue another which is more 
or less closely related to it, and arguing the substi- 
tuted issue. The fallacy does not take into account 
whether the arguments do or do not really support 
the substituted issue, it only calls attention to the 
fact that they do not constitute a proof of the orig- 
inal one. Su dents are quite often guilty of an 
ignoratio elenchi when in reply to questions they 
substitute some other though related question and 
allow their answers to be guided by it. It is a par- 
ticularly prevalent and subtle fallacy and it assumes 
a great variety of forms. But whenever it occurs 
and whatever form it takes, it is brought about by 
an assumption that leads the person guilty of it to 
substitute for a definite subject of inquiry another 
which is in close relation with it. In the petitio 
principii the fallacy may be described as an assump- 



576 A TEXT-BOOK OF LOGIC 

tion of the premises ; in the complex question, as an 
assumption of the answer; and in the ignoratio 
elenchi, as an assumption of the question at issue. 

Whenever, for any reason, a conclusion does not 
follow from the assigned premises, we have, in the 
literal sense of the term, a Non Sequitur. When 
used in this sense to include all the errors in reason- 
ing which leads to erroneous conclusions, the term 
is generic, and must be understood as synonymous 
with 'fallacy/ Any kind of loose or inconsequential 
argument, from this point of view, would be a non 
sequitur. 

More particularly considered, the fallacy of non 
sequitur, as was indicated by Aristotle, is the name 
we apply to the erroneous conclusion of a hypo- 
thetical syllogism. Aristotle regarded it as an 
"argument from the affirmation of the consequent," 
and for this reason it is sometimes called the fallacy 
of the consequent. If, for example, we argue that 
a particular individual who has no visible means of 
support must be a prefessional thief, because "if 
a man is a professional thief, he will have no visible 
means of support," the argument will be fallacious 
because, as we have seen, no conclusion can be 
reached by affirming the consequent of hypothetical 
propositions. The term non sequitur may also be 
applied to the other hypothetical fallacy of denying 
the antecedent. In both the cases to which the term 
has been said to apply, the assumption is made that 
the relation between antecedent and consequent of 
the major premise is causal, an assumption which 



FALLACIES 577 

we have no right to make in view of the complex 
interconnection of the facts with which our human 
knowledge has always to deal. But if it is made, 
the only way we can avoid a possible fallacy is to 
call into question the assumption, and thereby to 
raise definitely the question whether antecedent and 
consequent are causally connected or not. 

The attempt has sometimes been made to apply 
the name non sequitur to the fallacies which occur 
in connection with categorical arguments. This 
cannot be considered a useful employment of the 
term. For if the term applies to any and all of 
these errors, it must be regarded, as we have said 
above, as a generic term, and loses all particular 
significance, and if it is used of a particular kind 
of categorical fallacy, it immediately takes its place 
as a synonym of the name of that fallacy. Some 
logicians, however, do not take this view of the case, 
and they assign the term to a group of cate- 
gorical arguments of which the following may 
be said to be fairly representative : 'Episcopacy is 
of scriptural origin, the Church of England is the 
only established church in England, therefore the 
church established in England is the only church 
that should be supported.' Again, 'Pennsylvania 
contains rich coal and iron mines, Pennsylvania has 
no sea coast, therefore the battle of Gettysburg was 
fought in that state/ These examples are so flimsy, 
as examples of argument, that the only sensible 
course to take with regard to the class of reasoning 

37 



578 A TEXT-BOOK OF LOGIC 

for which they stand is to deny that it can have any 
logical recognition at all. Logic presupposes at the 
least some development of common sense on the 
part of those to whom it addresses itself, and one 
can hardly be expected to take so low an estimate of 
logic as to think that it can be of any possible service 
to the individual upon whom such so-called argu- 
ments would have the least chance to impose. The 
logician has absolutely nothing to do with such an 
individual who, in the interests of society, had much 
better be placed in the care of an alienist. 

We conclude, therefore, that non sequitur is a 
name that can be applied only to fallacies of the kind 
that occur in the course of hypothetical arguments. 
The fallacy consists in misinterpreting the implica- 
tions of the relation of antecedent and consequent 
stated in the major premise of hypothetical syllo- 
gisms. 

Fallacies of Interest. Knowledge, as we have 
shown, depends for one of its conditions upon what 
we call interest. But knowledge is not secured and 
advanced by any or any kind of interest. It is only 
when, as we have seen, the interest is directed 
toward, and is accompanied by a desire to ascertain, 
the nature and relations of the objects by which it 
is stimulated that it can be considered to be of 
service in the establishment of knowledge in the 
strict sense of that term. The interest that must be 
recognised as an indispensable condition of all 
knowledge whatever is specifically an interest that 
points toward and terminates in the establishment 



FALLACIES 579 

of the knowledge relation. Whenever any other 
interest than this is allowed, consciously or uncon- 
sciously, to influence the steps we take toward 
knowledge, or the conclusions we accept, the process 
and the conclusion are for that reason fallacious. 
Instances of the kind of argument just indicated 
will be considered in the following paragraphs, and 
they are grouped together because they all imply 
that some other interest has been substituted for 
the one which alone, as we have said, can be of 
service in the attainment of truth. 

Perhaps the most reputable of the fallacies of 
the kind in question is that which is known as post 
hoc, ergo propter hoc. In discussing the problems 
connected with the establishment of causal relations, 
we have seen that a succession of events is to be 
interpreted always as containing the suggestion of 
a possible causal connection between the events in 
question, or with other with which they are con- 
stantly associated ; but we saw also that the succes- 
sion itself is never to be taken as evidence of such 
connection. If, therefore, neglecting this latter con- 
sideration, we should argue from an observed suc- 
cession of events to the causal connection of the 
events, the conclusion would be fallacious because 
the only reason that could be assigned for the infer- 
ence, namely, that, since the one event had followed 
the other, it was, therefore, caused by that other, 
is never sufficient to establish a causal relation. The 
fallacy arises, then, from neglect of the negative 
criterion of causal relations to which we have just 



580 A TEXT-BOOK OF LOGIC 

referred, namely, that mere succession is never a 
sufficient reason for a causal inference. 

The relative prevalence of this fallacy, and the 
charitable attitude most of us take toward those who 
are guilty of it, suggest that the error which it 
implies lies somewhat deeper in the mental life than 
some others that have come before us. If this is 
true, the explanation and full exposition of the 
nature of the fallacy belong to psychology rather 
than to logic. In a general way, however, we can 
see that whenever the scientific interest, which seeks 
to safeguard conclusions from possible sources of 
error, is not strictly emphasised, or when it is for 
some reason temporarily weakened, it is easy for the 
human mind to slip into one of the more usual or 
conventional attitudes toward the objects of its ex- 
perience, and thus to arrive at conclusions which, 
to the extent that this has taken place, are fallacious. 
In these fallacies, we observe a tendency to confuse 
associative combinations with causal connections, a 
tendency which is emphasised whenever the prac- 
tical takes the place of the theoretical interest in 
determining our relations to the objects of our ex- 
perience. An example of this fallacy, frequently 
met with in educational circles, is the contention 
that because students who are handicapped by the 
necessity of earning their livelihood usually manage 
to pass their examinations, while others who are 
not so handicapped sometimes fail, the handicap is 
part of the cause of their success. In similar 
fashion, we have heard it argued that because Spur- 



FALLACIES 581 

geon, who never went to college, was a great 
preacher, that this was due to the fact that he never 
attended college. There is more common sense and 
logic in Spurgeon's remark, referring to the above 
contention, that the result was accomplished in 
spite of his lacking a collegiate training. 

There are a number of fallacies which are due 
still more obviously to the way in which arguments 
connect themselves with interests which are distinct 
from the one with which our search for truth is 
more particularly associated, and in which the con- 
clusion assumes a character in conformity with 
these interests. When, for instance, an argument 
makes an appeal to the character, principles, pro- 
fession, or interests of an individual, and it is ac- 
cepted or rejected for that reason, there results a 
fallacy which is called an argumentum, ad hominem. 
If, for example, the evidence for the movement of 
the earth round the sun is rejected because it is 
inconsistent with one's religious convictions, the 
rejection is fallacious because the argument reaches 
its conclusion by the substitution of the religious 
for the scientific interest. If, again, the fact that 
one owns stock in a brewery is allowed to influence 
his judgment as to what conclusion, with respect to 
the sale of alcoholic beverages, is warranted by the 
scientific evidence that is available on the physio- 
logical effects of alcohol on the human system, he is 
guilty of the fallacy under consideration. When, 
once more, the demands of religion upon the indi- 
vidual are rejected because preachers or church 



582 A TEXT-BOOK OF LOGIC 

members are not free from obvious faults, or when 
they are accepted because thereby business will be 
helped, the position in each case involves an ad 
hominem fallacy. 

The admission, by courts of law, of testimony 
bearing upon the character of witnesses, requires 
a word of explanation, because it seems to be in 
contravention of the recognised fallacious nature 
of the arguments we are now considering. The 
difficulty created by this instance is removed when 
we observe that courts of law do not admit testi- 
mony as to the character of witnesses for the pur- 
pose of deciding whether the verdict shall be for 
or against the plaintiff, but for the purpose of 
eliminating, from the evidence that comes before it, 
testimony that is irrelevant to the issue, that is, 
testimony which, because it is prejudicially affected 
by the character of the individual who gives it, 
involves an argumentum ad hominem. Prejudiced 
or perjured evidence is fallacious in exactly the 
sense in which any ad hominem argument is falla- 
cious. 

When an argument is accepted because it enlists 
on one side or other of the question at issue, our 
feelings, passions or prejudices, it is called an argu- 
mentum ad populum. This is essentially the fallacy 
of public address. Any cause, as we all know, that 
can bring impressive oratory and brilliant metaphor 
to its aid is very likely to secure the support of many 
upon whom the cause itself and the arguments which 
really support it, would have little or no influence. 



FALLACIES 583 

Conspicuous examples of fallacious reasoning of 
this kind may be found on almost every page of the 
voluminous writings of the late Robert Ingersoll. 
A somewhat similar fallacy is that which is known 
as argumentum ad misericordiam. In this case, our 
judgment is determined by the appeal that is made 
to our pity or sympathy. Whenever, for example, 
we recommend a cause by emphasising the plight of 
those whom it is intended to benefit, or give our sup- 
port because of our interest in the individuals who 
advocate it, or give alms to a beggar because he is 
in rags, we are guilty of letting our sympathy inter- 
fere with our judgment, and this is exactly what 
occurs in any argumentum ad misericordiam. 

The influence of a great name or of long estab- 
lished customs is pretty generally recognised as serv- 
ing a useful purpose in the development of the indi- 
vidual and the race. When, however, our reverence 
for individuals or institutions leads us to accept, 
without consideration of the arguments which may 
be advanced for and against them, positions which 
receive the support of or are in conformity with 
any established authority, we are said to be guilty 
of the fallacy, argumentum ad verecundiam. This 
is a fallacy to which the conservatives among us 
are particularly prone. Our interest in order, in 
things as they are, unless balanced by a due regard 
for change, may lead us to accept a position merely 
because it is in agreement with some established 
custom, or to reject another merely because it re- 
quires the rejection of some accepted authority. A 



584 A TEXT-BOOK OF LOGIC 

peculiarly aggravated form of the fallacy comes to 
light in those instances where an individual's right 
to speak with authority in one field of knowledge is 
taken as the ground of our acceptance of that indi- 
vidual's opinion in another field with respect to 
which he has no special acquaintance. "The pres- 
tige of a great name," as Creighton remarks, "is 
thus irrelevantly invoked when no significance prop- 
erly belongs to it. Thus, for example, a successful 
general is sometimes supposed to speak with author- 
ity upon problems of statescraft, and the opinions 
of prominent clergymen are quoted regarding the 
latest scientific or political theories." 

REFERENCES 

H. A. Aikins, The Principles of Logic, Chs. XVIII., XIX., XX. 
J. E. Creighton, An Introductory Logic, 3d Edition, Chs. 

XII., XX. 
J. G. Hibben, Logic, Deductive and Inductive, Part I., Ch. 

XIX., Part II., Ch. XVI. 
W. S. Jevons, Elementary Lessons in Logic, Lessons XX., 

XXI. 
S. H. Mellone, An Introductory Text-Book of Logic, 3d 

Edition, Ch. X. 
C. Read, Logic, Deductive and Inductive, 3d Edition, Ch. 

XXIV. 
W. J. Taylor, Elementary Logic, Ch. XVIII. 

ADVANCED 

W. R. B. Gibson, The Problem of Logic, Ch. XXVIII. 
H. W. B. Joseph, An Introduction to Logic, Ch. XXVII. 
J. S. Mill, A System of Logic. Book V. 
F. C. S. Schiller, Formal Logic, Ch. XXIII. 



FALLACIES 585 

A. Sidgwick, Fallacies. 

J. Welton, A Manual of Logic, Vol. II., Book VII. 

QUESTIONS 

1. What is an inductive fallacy, and into what classes 
may such fallacies be divided. 

2. What testimony can you quote showing the importance 
of a careful and accurate use of language for logical 
thinking? 

3. What did Bacon mean by Idols of the Market Place? 

4. How does Locke explain the fact that language often 
renders thought fallacious? 

5. In what two ways may the observation of facts be 
fallacious? 

6. State and illustrate the fallacy of insufficient observa- 
tion. 

7. What do you understand by a negative instance? 

8. What is the testimony of Bacon and Darwin as to the 
importance of negative instances? 

9. In what respect does education predispose one to the 
neglect of negative instances? 

10. What does Bacon mean by Idols of the Theatre? 

11. In what form is the fallacy described by Bacon in 
these terms likely to appear at the present day? 

12. What is the fallacy of incomplete or imperfect obser- 
vation? 

13. Explain how the personal factor may lead to incomplete 
or imperfect observation. 

14. In what way does technique affect the thoroughness of 
observation? 

15. What are the two fallacies of explanation considered 
in the text? 

16. Explain what is meant by a hasty generalisation. 

17. To what consideration of scientific importance does the 
possibility of hasty generalisations point? 

18. What is the fallacy of false analogy? 



586 A TEXT-BOOK OF LOGIC 

19. In what respect is the fallacy of false analogy similar 
to the fallacy of figurative language? 

20. In what respect does false analogy resemble the fallacy 
of negative instances? 

21. What is the general character of the fallacies of the 
context? 

22. Into what two classes may fallacies of the context be 
divided? Describe each class, naming the particular 
fallacies that belong therein. 

23. What do we mean by a fallacy of assumption? 

24. Describe the essential character of a petitio principii. 

25. How may we proceed to break down a petitio principii? 

26. How may a varepov irporepov be distinguished from a 
circulus in probando, and how are they related to a 
petitio principii? 

27. What is the fallacy of the complex question? 

28. What, according to Aristotle, is an ignoratio elenchi? 

29. What is an ignoratio elenchi according to modern logic? 

30. What is Aikin's term for an ignoratio elenchi, and dis- 
cuss its appropriateness. 

31. From the standpoint of the assumptions involved, how 
do the petitio principii, the complex question, and the 
ignoratio elenchi differ from one another? 

32. What is the genereic meaning of the non sequitur? 

33. What, according to Aristotle, is a non sequitur, and 
what, accordingly, is another name for the fallacy? 

34. With what meaning is the term non sequitur now used 
in modern logic? 

35. Discuss the relation of the non sequitur to categorical 
arguments. 

S6. What are the fallacies of interest? 

37. Describe the post hoc, ergo propter hoc fallacy. 

38. What is understood by an argumentum ad hominem? 

39. Does the admission of evidence as to the character of 
accused persons, or of those giving evidence, by courts 
of law involve the verdict in the ad hominem fallacy? 
Explain. 



FALLACIES 587 

40. What is the argumentum ad populum? Illustrate. 

41. State and illustrate the argumentum ad misericordiam. 

42. Show by means of illustrations the nature of the argu- 
mentum ad verecundiam. 

EXERCISES 

Examine the following arguments, and state in what re- 
spects, if any, they are fallacious, the technical name of 
the fallacy of which each is guilty, and the class to 
which the fallacy belongc: 

(1) In the act of landing on the African coast, Caesar 
accidentally stumbled, and, as he did so, he ex- 
claimed, 'Africa! I embrace thee.' Against what 
fallacy on the part of his followers was this ex- 
clamation intended to guard? 

(2) It is a dictum of the Cartesian philosophy that 
whatever can be clearly conceived exists. Is this 
fallacious, and if so, why? 

(3) The opponents of the Copernican system argued 
that if the earth moved, a stone let fall from the 
top of a tower would not reach the ground at the 
foot of the tower, but at a point some distance 
from it, in a direction opposite to the earth's 
movement. Such, however, is not the fact. 

(4) It is reported by travelers that the negroes among 
whom coral is worn as an amulet affirm that it is 
always affected by the state of health of the 
wearer, becoming pale in disease. This is not 
true. 

(5) Women, as a class, are supposed not to have 
hitherto been equal in intellect to men, therefore 
they are necessarily inferior. 

(6) The twenty-five years of Republican tariff legis- 
lation have been a nera of unparallelled prosperity. 
Why kill the goose that lays the golden eggl 



s?' 



588 A TEXT-BOOK OF LOGIC 

(7) The metropolis of a country may be compared to 
the heart of a living body, hence we may infer that 
any considerable increase in size of the metropolis 
is evidence of a diseased condition of the body 
politic. 

(8) The early Teutonic societies were held together 
by ties of kinship, because all societies were so 
held together originally. 

(9) It is sometimes contended that because punishment 
can only intimidate it is brutalising, and therefore, 
it should not be employed, but that only shows that 
there are persons who are so brutalised that they 
can be influenced only through fear. 

(10) The apologists of Charles I., McCaulay complains, 
defend the king by urging that he was a good 
judge of pictures and indulgent to his wife. 

(11) This is a party measure and therefore we must 
vote for it. 

(12) A religion which elevates the soul above the body 
can survive persecution, and since the Christian 
religion has survived persecution, it enables its 
devotees to prefer the interests of the soul to 
those of the body. 

(13) It is frequently assumed, because the animals and 
men native to countries of inclement climates, 
where the conditions of life are severe, are usually 
robust, that the hardships they are forced to 
undergo in youth are the cause of their hardiness. 

(14) I do not know that you will approve it, but I gave 
him a pair of shoes, an old coat, and something 
to eat. I felt so sorry for him. 



INDEX 



Abelard, on universals, 93 
Accent, fallacy of, 5l7f 
Accident, as predicable, 186 

converse fallacy of, 521 
fallacy of, 520f 
Acquipollence, education by, 279f 
Affirming the consequent, fallacy of, 

540f 
Agreement, Method of, 477f 

a method of observation, 

480, 482 * 
elimination and, 478 
Jevon's formulation of, 477 
limits of, 480f 
Mellone's formulation of, 

479 
method of single, 477 
method of double, 490 
Mill's formulation of, 477 
states an ideal, 479f 
Agreement and Difference, Method of, 
486f 
application of, 490f 
conditions of its use, 486f, 

496 
field of application, 487 
Melone's formulation of, 

489 
Mill's formulation of, 488 
Aikins, on the forgotten issue, 575 
Ambiguity, as fundamental logical 
problem, 164 
criticism of traditional 

view of, 163f 
fallacy and, 514 
judgment and, 54 
structural, 522f 



traditional view of, 162f 
translation and, 165f 
verbal, 515f 

of terms, fallacies of, 534f 
Ambiguous disjunction, fallacy of, 

547f 
Amphibole, fallacy of, 522f 
Analogy, conditions of, 413f, 417f 
false, fallacy of, 565f 
function of, in induction, 

416f . 
limits of,- 412f, 418 
logical character of, 411f, 

419f 
meaning of, 409f 
translation and, 165f 
Anselm, on universals, 93 
Aquinas, on universals, 93 
Arguments, basis of categorical, 297f 
categorical, 297f, 301f, 326f 
circular, 572 
constructive hypothetical, 

351f 
deductive, 532 
destructive hypothetical, 

353f 
dilemmatic, 354f 
disjunctive, 343f, 544f 
hypothetical, 348f, 539f 
inductive, 532 
logical problem of cate- 
gorical, 298 
mixed disjunctive, 343f 
simple disjunctive, 343f 
validity of disjunctive, 
345f 
Argumentum, a dicto secundum quid, 
521 



589 



590 



INDEX 



a dicto simpliciter, 520 
ad hominem, 581 
ad misericordiam, 583 
ad populum, 582f 
ad verecundiam, 583f 
Aristotle, list of Predicables, 181 
on analogy, 409 
on fallacies, 508 
on ignoratio Elenchi, 573 
on logic, 12, 18 
on non seguitur, 576 
on the categories, 369 
on the classification of fal- 
lacies, 511 
on the fallacy of division, 

519 
on what can be defined, 182 
Assertion, conditions of relevant, 36f 
grounded, 302 
grounds of, 302 
judgment as, 28f 
relevant, 36f 
truth and, 58 
Assumption, fallacies of, 569f 



Bacon, on Idols of the Market Place, 
553f 
on Idols of the Theatre, 559f 
on imperfect induction, 375 
on negative instances, 375, 557f 
on perfect induction, 374 
on the interrogation of nature, 

442 
the herald of modern learning, 
471 
Bosanquet, on negative terms, 152 
Bradley, on disjunction, 342 

on the real subject of judg- 
ment, 55 
on the 'that' and the 'what' 
of judgment, 49 
Brodie, on scientific imagination, 424 



Categories, defined, 369 

predication and, 369 
Causation, analysis and, 455f 

complex characts, of facts 

of, 449f 
elimination as a method of, 

474f 
hypothetical statements and, 

462f 
metaphysics of, 458f 
Mill's Methods and, 473f 
necessity and, 457f 
practical aspect of, 436f 
problem of, 435f, 442f, 451 f 
purpose and, 455 
reciprocal, 461, 473f 
relation of practical and 
theoretical aspects of, 
440f 
relation of purpose to, 449 
temporal sequence and, 445f 
theoretical aspect of, 43Sf 
Cause, analysis, 455f 

certainty and, 455 

complex character of, 449f, 

453f 
conditions and, 451 
effect and, 447f, 453f 
indeterminateness of, 452 
necessity of, 456f 
occasion and, 451 
probability and, 464f 
purpose and, 449, 455 
reciprocity of effect and, 461f 
temporal antecedence and. 445f 
Causes, composition of, 499 

criticism of plurality of, 465f 
permanent, 486 
plurality of, 461f, 542f 
Classification, artificial, 215 

comparison and, 212f, 

377 
conditions of, 214f 
defined, 211f 
definition and, 212f 



INDEX 



591 



division and, 213f 
induction and, 215 
kinds of, 215f 
Mill's doctrine of, criti- 
cised, 216 

natural, 215 
practical, 2l7f 
purpose and, 214, 216f 
scientific and popular, 

377f 
statistical methods and, 

391f 
theoretical, 217 
Colligation, nature of, 378f 

value of, 380 
Comparison, classification and, 214 
definition and, 169, 190 
relation of judgment and 
reasoning to, 303 
Complex Question, fallacy of, 572f 
Composition, converse fallacy of, 519 

fallacy of, 518f 
Concept, conceptualist view of, 93 
logical view of, 93f 
nominalist view of, 93 
psychological view of, 93 
realist view of, 92f 
Conclusion, as grounded assertion, 302 

defined, 304 
Concomitant Variations, Method of, 
486, 492f 
conditions of its use, 

493, 494f, 497 
field of its application, 

496 
Mill's formulation of, 

492 
quantitative phenomena 

and, 494f 
the principle of, 493 
Conditions, cause and, 451 

essential, 456 
Context, relation of judgment and 
proposition to, 54, 82, 87 



Contradiction, basis of, 211 
fallacy of, 527 
meaning of, 272f 
Contradictories, meaning of, 210 
Contraposition, education by, 288f 

table of, 289 
Contrariety, meaning of, 266f 
Connotation, meaning of, 109f, 158 
of collective term, 128 
of general term, 125 
of individual term, 122f 
of positive term, 144f 
problems of, 117, 158 
relation to denotation, 
llOf 
Conversion, contrapositive, 288f 
fallacies of, 530f 
meaning of, 283f 
method of, 284f 
per accidens, 286 
rule of, 285 
simple, 285f 
table of, 288 
Copula, as "sign of predication", 94, 
234 
existential views of, 95f 
function of, 91f, 234 
how expressed, 91 
relational view of, 92f 
Creighton, on argumentum ad vere- 
cundiam, 584 
on fallacy of accent, 618 
on the Joint Method, 487f, 

491f 
on the connotation of 
proper names, 122 



Darwin, on theorising, 399 

on negative instances, 558 
Definition, classification and, 212f 

comparison and, 109, 190, 

212f 
conditions of, I67f 
convertible with definien- 
dutn, 179 



»*' 



592 



INDEX 



dichotomy and, 207f 
elementariness of, I79f 
genetic, 176 
homogeneity of terms in, 

179 
indeterminateness of, 196f 
negative, 180f 
per genus et differentiam, 

171f 
positive, 180 
problem of, 159, l80f 
real, I73f 
relation of division to, 190, 

198f 
relation of purpose to, 

175f 
structural, 175 
synonyms and, 180 
tests of, I76f 
too broad, l77f 
too narrow, 178 
verbal, l73f 

when employed, 167f, 170, 
190 
Denotation, meaning of, 108f, 114f 
of collective term, 128f 
of general term, 125 
of individual term, 122f 
of positive term, 144f 
problems of, 117, 158 
relation to connotation, 
HOf 
Denying the antecedent, fallacy of, 

540f 
Designation, as concrete term, 121 
meaning of, I22f, 124 
Dichotomy, definition and, 207f 
division by, 205f 
nature of, 206f, 210 
value of, 208f 
Difference, Method of, 482f 

a method of experiment, 

482 
grounds of validity, 485f 
indirect method of, 490 
intermixture of effects and, 
485 



Mellone's formulation of, 

484 
Mill's formulation of, 482 
single method of, 484 
Differentia, as predicable, 185f 

meaning of, 172f 
Dilemma, classes of, 357f 

constructive, 357f 
defined, 355 
destructive, 858f 
nature of, 354f 
structure of, 356f 
validity of, 359f 
Distributed, meaning of, 114f 

terms in categorical prop- 
osition, 259f 
Disjunction, basis of, MOi 
exclusive, 341f 
exhaustive, 342f 
Division, by dichotomy, 205f 

classification and, 213f 
conditions of, 213f 
cross, 201 
fallacy of, 519f 
logical, exhaustive, 205 
meaning of logical, 191f, 193, 

195 
metaphysical, 194 
physical, 195 
principle of, 195, 196f 
rules of logical, 192, f, 200f 
terminology of logical, 199f 
verbal, 195 



E 



Eductions, by aequipollence, 279f 
by contraposition, 288f 
by conversion, 283 
by inversion, 290f 
by negation, 288f 
by obversion, 279f 
by permutation, 279f 
classes of, 279f 
fallacies of, 529f 
meaning of, 278f 



INDEX 



593 



schema of, 292 
summary of, 291 
table of, 292 
Effect, cause and, 447f 

conditions and, 461 

intermixture of, 485f, 499 

nature of, 452 

occasion and, 451 

reciprocal character of cause 

and, 461f 
temporal sequence and, 445f 
Enthymeme, denned, 328 

elliptical nature of, 329 
Figure of, 329 
Mood of, 329 
Orders of, 328 
syllogistic character of, 
328 
Enumeration, generalisation and sim- 
ple, 386 
simple, 375f 
Episyllogism, polysyllogism and, 330 
Epicheirema, nature and classes of, 

335f 
Equivocation, fallacy of, 515f 
Error, characteristic of assertion, 58 
compatibility of asserted con- 
tent in, 68f 
conditions of, 82, 97 
not irrelevance, 65f 
purpose and, 66 
Exclamations, logic of, 31f 
Experiment, controlled conditions, 403 
limitations of, 401 
nature of scientific, 400, 

402f, 483f 
observation and, 400 
relation of purpose to, 

402f 
scientific 402f, 483 



Fact, a coexistent, 486 

colligation and, 378f 
meanings of, 367f 

♦38 



relation to judgment, 368 

relations of, 370f 

world of, 37lf 
Fallacies, categorical, 533 

classification of, 511f 

deductive, 533f 

defined, 508f 

disjunctive, 544f 

hypothetical, 539f 

inductive, 552f 

a dicto secundum quid, 521 

a dicto simpliciter, 520 

ad hominem, 581 

ad tnisericordiam, 583 

ad populum, 582f 

ad verecundiam, 583f 

categorical, 533 

classification of, 511f 

deductive, 633f 

defined, 508f 

disjunctive, 544f 

hypothetical, 539f 

ignoratio elenchi, 573 

inductive, 552f 

non sequitur, 576f 

of accent, 5l7f 

of accident, 520f 

of accident, converse, 521f 

of ambiguous disjunction, 

547f 
of amphibole, 522f 
of assumption, 569f 
of complex question, 572f 
of composition, 518f 
of contrariety, 627f 
of conversion, 530f 
of division, 519f 
of eduction, 529f 
of education, 529f 
of equivocation, 615f 
of explanation, 563f 
of false analogy, 565f 
of false disjunction, 545 
of false parenthesis, 524 
of four terms, 534f 
of hasty generalisation, 663f 



594 



INDEX 



of incomplete disjunction, 

645f 
of implication, 625f 
of inference, 631f 
of insufficient premises, 537f 
of interest, 578f 
of interpretation, 614f 
of language, 653f 
of observation, 655f 
of obversion, 529f 
of opposition, 526f 
of subalternation, 628f 
of subcontraiety, 627f 
of the consequent, 676 
of the context, 567f 
petitio principii, 670f 
post hoc, 679f 
structural ambiguity and, 

522 
verbal ambiguity and, 615 

G 

Generalisation, causal sequence and 
empirical, 463f 
classification and, 377f 
empirical, 376f, 38Sf 
hasty, fallacy of, 563f 
Mill on, 378 
presuppositions of, 377 
simple enumeration 

and, 386 
statistical methods 

and, 391f 
value of empirical, 
378, 385 
Genus, meaning of, l72f 

as predicable, 185f 
Gibson, on elimination in causal in- 
quiries, 476f 
on experimentation, 403 
on statistical method, 391 
Green, on colligation, 379 
Grote, on knowledge of acquaintance 
and knowledge about, 83 



H 

Hegel, on the syllogism of analogy, 412 
Herschel, his contributions to induc- 
tive logic, 472 
on residual phenomena, 600 
Huxley, on intellectual observation, 

400 
Hobbes, on language, 553 

on the scientific imagination, 
426 
Hypothesis, analysis and, 421 

imagination and, 426f 
limits of, 420f 
living, 427 
nature of, 420 
objections to, 422f 
theory and, 429f 
truth and, 427 
verification of, 427f 



Imagination, science and,424f 
Imperatives, logic of, 31f 
Implication, classes of, 264f 
fallacies of, 526f 
meaning of, 263f, 278, 626f 
Induction, analogy and, 416f 

explanatory methods of, 

406f 
ground of truth of, 387f 
hypothetical statements and, 

389 
imperfect, 373 
number of instances and, 

386, 386f, 555 
perfect, 372, 376f 
problem of, 366f, 372 
simple enumeration and, 

372f 
two factors of, 386f 
Inference, by private conception, 279f 
fallacies of, 631f 
immediate, 263f. 

Instances, negative, 375, 484f, 556f 
positive, 484f 



INDEX 



595 



Intelligence, nature and development 
of, 395f 

Interest, assertion and, 36f 

cansation and, 449, 455 
classification and, 214, 216f 
designation and, I23f 
error and, 66 
experiment and, 402f 
general term and, 125f 
judgment and, 44f, 67, 117 
knowledge and, 44f, 578f 
meaning and, 117 
and opinion, 464 
observation and, 397, 402f. 

Interrogatives, logic of, 31f 

Inversion, method and nature of, 290 
obversion and, 291 
tables of, 291 

Irrelevance, nature and forms of, 65f 

J 

James, definition of conception, 26 

on knowledge of acquaintance 

and knowledge about, 83. 
on the meaning of term 
thought, 25 
Jevons, on analogy, 419 

on ignoratio etenchi, 574f 
on imperfect induction, 374f 
on the antecedent of causal 

events, 450f 
on the dilemma, 359 
on the fallacy of accent, 517 
on the intermixture of effects, 

499 
on the Method of Single 

Agreement, 477 
on the occasion of an event, 
451 
Joseph, on elimination in causal in- 
quiries, 474f 
Judgment, actual subject of, 52, 55 
ambiguity of, 54f 
as assertion, 28f, 29f, 36f 
as grounded assertion, 302 
belief and, 97 



comparison and, 303 
conditions of, 36f 
content of, 29, 82 
defined, 29, 50, 65 
difference and, 240 
empirical, general, 385f 
enumerative, 374 
error and, 65f 
fact and, 368 
fragmentariness of, 83, 87 
groundless statements and, 

33f 
identity and, 239 
incompleteness of, 54 
interest and, 44f, 67, 117 
limits of, 67 
logical subject of, 52. 

mental attitudes akin to, 

31f 
nature of, 28f, 35f, 51, 55, 
303 

object of, 47f, 50, 368 

objective of, 50 

origin of, 77f 

practical aspect of, 357 

presupposition of, 52, 97 

probable, 62f 

proposition and, 76f, 84, 94, 
303 

scientific, and probability, 
62f 

social, and probability, 62f 

subject-matter of, 29, 47f 

theoretical aspect of, 35f, 
41f 

thought and, 28f 

truth of, 58f 



Knowledge, about, 83 

error and, 65f 
interest and, 44f, 578f 
meaning of, 5f 
method of, logic as, 20 
of acquaintance, 83. 
opinion and, 464 



596 



INDEX 



relation of syllogism to, 

298f 
systematic, 6f, 391f 
truth and, 58f, 60f, 366 
Knowledges, logic and the, 9f, 18 
meaning of, 9 
thought and the, lOf 



Language, Hobbes on, 553 

judgment and, 76, 84f, 96, 

98f 
Locke on, 554f 
the sciences and, 160 

Locke, on language, 554f 

Logic, as an art, 17f, 20f. 

as method of thinking, 19 
as science, 21f 
as science of meaning, 20 
as scientia scientiarum, llf 
as scientific method, 19 
Herschel's contributions, 472 
humanistic influence in, 12f 
Mill's historical position of, 472 
psychology and, 14f, 20 
subject-matter of, If, lOf 
the knowledges and, 9f 
the sciences and, lOf 
thought and, lOf 

Lotze, on observation, 400 

M 

Major, ambiguous, fallacy of, 634 

illicit process of, 536 
Market place, idols of, 553f 
Mathematical proportion, analogy and 
400f 
syllogism and, 300f 
Meaning, absolute and relative, dis 
tinction between, 140f 
abstract, 130f 

abstract, development of 
134f 



abstract, partial views of, 

131f 
collective, 126f 
concrete, 118, 130f 
concrete and abstract, basis 
of distinction between, 
139 
contrary, 155 
disparate, 155 
general, 124f, 126 
incompatible, 238 
individual, 124f 
individual concrete, kinds 

of, 121f 
interest and, 117 
negative, 143f, 236f 
negative, conditions of, 

145f 
negative interpretation of, 

149f, 154 
positive, 143, 235f 
privative, 143f, 236f 
Meinong, on object and objective of 

judgment, 49f 
Mellone, on analogy, 416 

on denying the antecedent, 

542 
on induction, 416 
on the Joint Method, 489 
on the Method of Agree- 
ment, 479 
on the Method of Differ 
ence, 484 
Methods, experimental, their historical 
position, 471f 
problem to which they apply, 

473f, 496 
statement of, 477f 
Middle, ambiguous, fallacy of, 534 

undistributed, 536 
Mill, his meaning of unconditional, 
459f 
historical position of his Logic, 

47lf 
on analogy, 419 
on a philosophical language, 553 



INDEX 



597 



on causation, 444f 

on colligation, 378f 

on empirical generalisation, 376 

on hypothesis, 427 

on imperfect induction, 375 

on invariable sequence, 445f 

on parity of reasoning, 381 

on perfect induction, 374 

on permanent causes, 486 

on purpose and cause, 449 

on the complex character of 

causal events, 449f, 457 
on the composition of causes, 



Negation, bare, 152 

conditions of, 145f 
double, 279 
eduction by, 288f 
function of, 238 
meaning of, 149f, 153f, 24 
Non-ambiguity, division and, 190f 
fallacy and, 515 
language and, 160 
limits of, 161f 
Nonsense, logical status of, 238 
Non sequitur, fallacy of, 576f 



on the connotation of proper 

names, 12f 
on the copula, 95f 
on the intermixture of effects, 

485f 
on the Joint Method, 486f 
on the necessity of causal 

events, 456f 
on the plurality of causes, 461f 
on the relation of metaphysics 

to causal problems, 458f 
on the Method of Agreement, 

477f 
on the Method of Concomitant 

Variations, 492f 
on the Method of Difference,. 

482f 
on the Method of Residues, 496f 
on the Methods of Experimen- 
tal inquiry, 47lf 
Minto, on Aristotelian logic, 13, 21 
on the history of logic ,471 

N 

Names, connotation of proper, 112, 
121f 

denotation of proper, 121 

meaning of, 88f 

terms and, 88 
Necessity, causal, 457f 



Object, affected by mode of apprehen- 
sion, 24f 
implication of, in conscious 

process, 24f 
meaning of, 24 
Observation, analytic character of, 
398f 
development of, 395f 
experimental, 400f, 453 
experimental, limits of, 

401 
imagination and, 426 
limits of, 555, 556f 
perceptual, 396f 
qualitative methods of, 

of, 399f 
scientific, 397f 
scientific and Method 

of Residues, 500 
selective character of, 

399f 
theoretical, 401f, 453 
Obversion, fallacy of, 529f 
meaning of, 279f 
method of, 281f 
rules of, 290 
table of, 282 
Occasion, meaning of, 451 
Opposites, contradictory, 210 
Opposition, contradictory, 272f 
contrary, 266f 
fallacies of, 526f 



) 



<* 



0o 



598 



INDEX 



kinds of, 266 
meaning of, 265 
subaltern, 269f 
subcontrary, 273f 
square of, 275f 
table of, 279 
Optatives, logic of, 31f 



Pearson, on the objectivity of science, 

423 
Permutation, education by, 279f 
Petitio principii, fallacy of, 570f, 573 

575f 
Polysyllogism, defined, 330 

progressive, 331 
prosyllogism and, 330 
regressive, 331 
types of, 33lf 
Post hoc, fallacy, 679f 
Porphyry, list of Predicables, 181 

on the subject of predica 

tion, 182 
Tree of, 210f 
Predicables, Aristotle on, 181f 
commensurate, 183 
lists of, 181 
meaning of, 181 
non-commensurate, 183 

185f 
Porphyry on, 181f 
problem of, 160, 181f 
Predication, basis of, 239 

categories and, 369 

degrees of, 222 

kinds of thing and, 160 

181f 
meaning of, 85f, 222 
Premises, as grounds of assertion, 302 
function of, 305 
major and minor, 305 
negative, fallacy of, 537f 
particular, fallacy of, 537f 
propositions as, 304f 



Probability, causation and, 464f 

characteristic of assertion, 

58 
conditions of, 62f 
scientific judgments and, 
62, 64f 
Propositions, affirmative, 235f, 238f 

affirmative and negative, 

relation of, 238f 
analysis of, 84f 
apodeictic, 250f 
as premises, 304 
assertoric, 247f 
categorical, 99, 102f 
categorical, classification 

of, 222f 
categorical, implications 

of, 255f 
causation and hypothet- 
ical, 462f 
compound, 244f 
compound hypothetical, 

355f 
context and, 82 
contraposition of, 288f 
degrees of certainty of, 

247 
distribution and the cate- 
gorical, 259f 
disjunctive, 99, lOOf 
eductive, 278f 
eductive, fallacies of, 

529f 
eductive, schema of, 292 
eductive, table of, 292 
exclusive, 241, 243f 
exceptive, 241 f 
exponible, 244 
hypothetical, 347f 
hypothetical, and causa- 
tion, 462f 
ideas and, 77 
import of, 79f 
indesignate, 232f 
induction and hypotheti- 
cal, 389 



INDEX 



599 



interpretation of, 263f 
inversion of, 290f 
judgment and, 76f, 84, 

803 
kinds of, 98f 
meaning of, 76, 85, 96, 

98f 
modality of, 235, 246f 
negative, 236f 
opposed, 265f 
opposed, fallacies of, 526f 
opposed, table of, 279 
opposition of, 265f 
origin of, 78f 
particular, 230f 
problematic, 248f 
quality of, 224f, 234f, 259f 
quality and quantity, re- 
lation of, 255f 
quantity of, 224, 225f, 259 
relations of, 222f, 225 
simple hypothetical, 99, 

lOlf 
singular, 228f 
statement— import of, 79f, 

84 
structural formulae of, 

256f 
terms and, 84f, 107 
the sentence and, 85 
truth— import of, 79, 84 
types of, 222f 
universal, 229f 
universal, kinds of, 230 
Proprium, meaning of, I84f 
Prosyllogism, polysyllogism and, 330 
Psychology, definition of, 26 
logic and, 14f, 20 
of thought, 25f, 35f 
Purpose, see Interest 
Pythagoras, on the mathematical in- 
terpretation of nature, 393 



Quantity, of propositions, 224, 225f, 

269 
Quality, of propositions, 224f, 234f, 259f 



Reality, belief in, 97 

judgment and, 52, 55 
meaning of, 370f 
spheres of, 97f 
Reasoning, parity of, 380f 
Residues, Method of, 496f 

intermixture of effects and, 

498f 
Mill's formulation of, 498 
scientific observation and, 
500 
Roman Church, realism of, 93 
Roscellinus, on universals, 93 

s 

Schoolmen, on universals, 92 
Sciences, aims of the, 406f, 423 

co-operation in the, 562f 
imagination and the, 424f 
language and the, 160 
method of, logic as, 19 
nature of the, 21 
objectivity of the, 423 
starting point of the, 443f 
subject-matter of, If 
thought and the, 2f 
Series, causal, 448f 

continuous, 203 
Sidgwick, an analogical reasoning, 566 
on petitio principii, 570 
on subject and predicate 
terms, 87 
Sorites, Aristotelian, 332 
defined, 332 
Goclenian, 332f 
rules of, 335f 
Statistical Methods, as methods of 
observation, 393 






So 



600 



INDEX 



empirical generalisation 

and, 391f 
induction and, 391f 
logical character of, 389f 
quantitative, 392f 
Subalternation, fallacies of, 528f 
meaning of, 269f 
Subcontrariety, fallacies of, 526f 
meaning of, 273f 
Syllogism, as method, 299, 306 
categorical, 297f, 326f 
categorical, Figures of, 310f 
categorical, Moods of, 315f 
disjunctive, 343f 
disjunctive, Moods of, 344f 
disjunctive, validity of, 345f 
hypothetical, 348f, 539f 
hypothetical, Moods of, 350f 
judgment and, 298f 
major term and, 304 
mathematical proportion 

and, 300f 
minor term and, 304 
mixed disjunctive, 343f 
nature of, 301f, 326, 538f 
problem of, 298f 
propositions and, 304 
place of conclusion in, 301f 
quality of propositions in, 

307f 
quantity of propositions in, 

308f 
relation of Moods to Fig- 
ure in, 318f 
relation of premises to, 302 
rule of disjunctive, 344 
rules of categorical, 305f 
rules of Figures in cate- 
gorical, 312f 
simple disjunctive, 343f 
structural view of cate- 
gorical, 303f 
two ways of regarding, 326f 
valid Moods of categori- 
cal, 816f, 346 



Tautology, logical status of, 238, 240 
Terms, absolute, 141 

abstract, 130f 

classification of, 169 

collective, 128f 

common, 125f 

complementary, 211 

concrete, 118, 119f 

connotative use of, 109f 

contradictory, 529f 

contradictory opposite, 210 

contrary, 155, 529 

correlative, 143 

definition of, 159 

denotative use of, 108f, 114f 

designations as, 122f 

disparate, 155 

distribution of, 114f, 116 

extent of, 115 

fallacies of, 534f 

general, 126f, 213 

indefinite, 151 

indesignate, 151 

indeterminate, 211 

individual, 120f, 126, 141 

individual collective, 129 

infinite, 151 

many worded, 91 

names and, 88f 

negative, I51f, 154, 237f 

positive, 144 

predicate, 85, 86f, 237 

privative, 153f 

problems of the connotative 
and denotative use of, 117, 
158 

proper names as, 121f 

propositions and, 85, 107, 234 

relation of connotative and 
denotative use of, HOf 

relation of individual to gen- 
eral collective, 130 

relative, 141f 

sign of distributed, 115 

sign of undistributed, 116 



INDEX 



601 



single-worded, 91 
singular, I20f, 126 
subject, 85, 86f 
syllogism and, 304 
thing and concrete, 118f 
width of, 115 
Theatre, idols of, 559f 
Theory, hypothesis and, 429f 
Thing, concrete term and, 118f 
meaning of, 119 
predication and kinds of, 160, 
181f 
Thorndike, on statistics of individuals, 

390f 
Thought, as assertion, 28 

comparison and, 303 
conditions of systematic, 7f 
content and, 29 
immediate, 303 
judgment and, 28f 
knowledge and, 2f 
logical meaning of, 26f, 28 
logic and, lOf 
mediate, 303 
method of, logic as, 29 
nature of, 2f, 28 
practical aspect of, 35f 
syllogistic, 304 
theoretical aspect of, 35f 
uses of the term, 25f 
Translation, ambiguity and, 165f 

when employed, 166f 
Truth, assertion and, 58 
fact and, 366f 

grounds of, in induction, 387f 
hypothesis and, 427 
nature of, 58f 
systematic, 367 
syllogism and, 327 



tests of, 59, 60f 
the proposition and, 76f 
Tyndall, on the proof of an induc- 
tion, 427 
on the scientific imagination, 
422, 424, 426 

u 

Unconditional, meaning of, 459f 

necessity and, 456f 
Undistributed, meaning of, 115 
Universals, problem of, 92 
Universe of Discourse, indeterminate- 
ness of, 53f 
nature of, 52f 
plurality of, 57f 
relation of judgment and 
proposition to, 54, 82, 87 
varepov irpoTepov, fallacy of, 572 



Verification, of hypothesis, 427f 

the test of truth, 59, 60f 

w 

Welton, on ignoratio elenchi, 574 

on experimentation, 403 
Whateley, on ignoratio elenchi, 574 
on petitio principii, 572 
Whewell, his contribution to inductive 
logic, 472 
on colligation, 378f 
on practical inferences, 397 
Words, categorematic, 90 

indefiniteness in meaning of, 

161f 
logical classification of, 90 
significant, as terms, 89, 160 
syncategorematic, 90 



H 152 82 



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